Orientifold/Flux String vacua, supersymmetry breaking and Strings at the LHC. Dieter Lüst, LMU (Arnold Sommerfeld Center) and MPI München

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1 Orientifold/Flux String vacua, supersymmetry breaking and Strings at the LHC Dieter Lüst, LMU (Arnold Sommerfeld Center) and MPI München

2 I) Introduction Geometry: Calabi-Yau spaces, mirror symmetry, generalized spaces, D-branes, K-theory,... Black Hole Entropies String Theory SUSY field theories Particle physics, astrophysics, cosmolgy

3 Introduction: Count the number of consistent string vacua Vast landscape with N sol = vacua! (Kawai, Lewellen, Tye (1986); Lerche, Lüst, Schellekens (1986); Antoniadis, Bachas, Kounnas (1986); Douglas (2003),...)

4 Introduction: Count the number of consistent string vacua Vast landscape with N sol = vacua! (Kawai, Lewellen, Tye (1986); Lerche, Lüst, Schellekens (1986); Antoniadis, Bachas, Kounnas (1986); Douglas (2003),...) Two (complementary) issues:

5 Introduction: Count the number of consistent string vacua Vast landscape with N sol = vacua! (Kawai, Lewellen, Tye (1986); Lerche, Lüst, Schellekens (1986); Antoniadis, Bachas, Kounnas (1986); Douglas (2003),...) Two (complementary) issues: Can we view into the landscape? information about other vacua?

6 Introduction: Count the number of consistent string vacua Vast landscape with N sol = vacua! (Kawai, Lewellen, Tye (1986); Lerche, Lüst, Schellekens (1986); Antoniadis, Bachas, Kounnas (1986); Douglas (2003),...) Two (complementary) issues: Can we view into the landscape? information about other vacua? Can we by-pass the landscape? look for green (promising) spots - model independent predictions?

7 Strategy for string phenomenology:

8 Strategy for string phenomenology: Consider (only) those vacua that realize the Standard Model (by-pass the landscape problem):

9 Strategy for string phenomenology: Consider (only) those vacua that realize the Standard Model (by-pass the landscape problem): Go to the field theory limit - decouple gravity! M Planck /M FT

10 Strategy for string phenomenology: Consider (only) those vacua that realize the Standard Model (by-pass the landscape problem): Go to the field theory limit - decouple gravity! M Planck /M FT Are there model independent predictions beyond the SM?

11 Strategy for string phenomenology: Consider (only) those vacua that realize the Standard Model (by-pass the landscape problem): Go to the field theory limit - decouple gravity! M Planck /M FT Are there model independent predictions beyond the SM? But this is not a real test of string theory in itself!

12 Strategy for string phenomenology: Consider (only) those vacua that realize the Standard Model (by-pass the landscape problem): Go to the field theory limit - decouple gravity! M Planck /M FT Are there model independent predictions beyond the SM? But this is not a real test of string theory in itself! Can we test stringyness of physics? Measure excited string states in experiment?

13 Strategy for string phenomenology: Consider (only) those vacua that realize the Standard Model (by-pass the landscape problem): Go to the field theory limit - decouple gravity! M Planck /M FT Are there model independent predictions beyond the SM? But this is not a real test of string theory in itself! Can we test stringyness of physics? Measure excited string states in experiment?

14 Outline Intersecting D-brane models (type II orientifolds) (Lecture I) Intersecting brane models and their statistics D-instantons: non-perturbative couplings Stringy signatures at LHC (Lecture II) (The LHC string hunter s companion)

15 I) (Intersecting) D-brane models: (Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez, Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001);...)

16 I) (Intersecting) D-brane models: (Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez, Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001);...) Consider open string compactifications with intersecting D-branes Type IIA/B orientifolds:

17 I) (Intersecting) D-brane models: (Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez, Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001);...) Consider open string compactifications with intersecting D-branes Type IIA/B orientifolds: Gravitons live as closed strings in 10-dimensional lower space time (10-dim. bulk).

18 I) (Intersecting) D-brane models: (Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez, Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001);...) Consider open string compactifications with intersecting D-branes Type IIA/B orientifolds: Gravitons live as closed strings in 10-dimensional lower space time (10-dim. bulk). Non-Abelian gauge bosons live as open strings on lower dimensional world volumes π of D-branes.

19 I) (Intersecting) D-brane models: (Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez, Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001);...) Consider open string compactifications with intersecting D-branes Type IIA/B orientifolds: Gravitons live as closed strings in 10-dimensional lower space time (10-dim. bulk). Non-Abelian gauge bosons live as open strings on lower dimensional world volumes π of D-branes. Chiral fermions are open strings on the intersection locus of two D-branes: N F = I ab #(π a π b ) π a π b

20 I) (Intersecting) D-brane models: (Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez, Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001);...) Consider open string compactifications with intersecting D-branes Type IIA/B orientifolds: Gravitons live as closed strings in 10-dimensional lower space time (10-dim. bulk). Non-Abelian gauge bosons live as open strings on lower dimensional world volumes π of D-branes. Chiral fermions are open strings on the intersection locus of two D-branes: N F = I ab #(π a π b ) π a π b (Includes F-theory constructions) (Beasly, Heckman, Marsano, Saulina, Schafer-Nameki, Vafa; Donagi, Wijnholt,...)

21 I) (Intersecting) D-brane models: (Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez, Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001);...) Consider open string compactifications with intersecting D-branes Type IIA/B orientifolds: Gravitons live as closed strings in 10-dimensional lower space time (10-dim. bulk). Non-Abelian Hierarchy gauge bosons of live dimensions as open strings! on lower dimensional world volumes π of D-branes. Chiral fermions are open strings on the intersection locus of two D-branes: N F = I ab #(π a π b ) π a π b (Includes F-theory constructions) (Beasly, Heckman, Marsano, Saulina, Schafer-Nameki, Vafa; Donagi, Wijnholt,...)

22 I) (Intersecting) D-brane models: (Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez, Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001);...) Consider open string compactifications with intersecting D-branes Type IIA/B orientifolds: Gravitons live as closed strings in 10-dimensional lower space time (10-dim. bulk). Non-Abelian Hierarchy gauge bosons of live dimensions as open strings! on lower dimensional world volumes π of D-branes. Chiral fermions are open strings on the intersection locus of two D-branes: N F = I ab #(π a π b ) π a π b (Includes F-theory constructions) (Beasly, Heckman, Marsano, Saulina, Schafer-Nameki, Vafa; Donagi, Wijnholt,...) ( Heterotic constructions: Talks by Faraggi, Rizos, Vaudrevange)

23 Perturbative type II orientifolds contain: (Review: Blumenhagen, Körs, Lüst, Stieberger, hep-th/ )

24 Perturbative type II orientifolds contain: (Review: Blumenhagen, Körs, Lüst, Stieberger, hep-th/ ) Closed string 6-dimensional background geometry: M 10 = R 3,1 M 6 -Torus, orbifold, Calabi-Yau space, generalized spaces with torsion,... - Background fluxes: H3 NS, Fp R, ω geom

25 Perturbative type II orientifolds contain: (Review: Blumenhagen, Körs, Lüst, Stieberger, hep-th/ ) Closed string 6-dimensional background geometry: M 10 = R 3,1 M 6 -Torus, orbifold, Calabi-Yau space, generalized spaces with torsion,... - Background fluxes: H NS 3, F R p, ω geom Space-time filling D(4+p)-branes wrapped around internal p-cycles plus orientifold planes: - Open string matter fields.

26 Perturbative type II orientifolds contain: (Review: Blumenhagen, Körs, Lüst, Stieberger, hep-th/ ) Closed string 6-dimensional background geometry: M 10 = R 3,1 M 6 -Torus, orbifold, Calabi-Yau space, generalized spaces with torsion,... - Background fluxes: H NS 3, F R p, ω geom Space-time filling D(4+p)-branes wrapped around internal p-cycles plus orientifold planes: - Open string matter fields. Strong consistency conditions: - tadpole cancellation with orientifold planes. - space-time supersymmetry (brane stability)

27 Perturbative type II orientifolds contain: (Review: Blumenhagen, Körs, Lüst, Stieberger, hep-th/ ) Closed string 6-dimensional background geometry: M 10 = R 3,1 M 6 -Torus, orbifold, Calabi-Yau space, generalized spaces with torsion,... - Background fluxes: H NS 3, F R p, ω geom Space-time filling D(4+p)-branes wrapped around internal p-cycles plus orientifold planes: - Open string matter fields. Strong consistency conditions: - tadpole cancellation with orientifold planes. - space-time supersymmetry (brane stability) (diophantic equations with finite no. of solutions!)

28 Orientifold with space-time filling D-branes: IIA: special lagrangian submanifolds: D6 on 3-cycles at angles Mirror symmetry (SYZ) IIB: points, (complex lines), divisors, (CY) with gauge bundles D3 (D5) D7 (D9)

29 Orientifold with space-time filling D-branes: IIA: special lagrangian submanifolds: D6 on 3-cycles at angles Mirror symmetry (SYZ) IIB: points, (complex lines), divisors, (CY) with gauge bundles D3 (D5) D7 (D9)! M Orientifold projection: M 10 =(R 3,1 M 6 )/(Ω σ) IR (3,1) Ω : σ : world sheet parity spatial reflection D6 O6 D6

30 Realization of the SM with G=SU(3) x SU(2) x U(1) and 3 generations of quarks and lepton: SM Soft SUSY breaking HS

31 Realization of the SM with G=SU(3) x SU(2) x U(1) and 3 generations of quarks and lepton: SM Soft SUSY breaking (b) left g HS (c) right U(3) Natural D-brane quiver of the SM: (a) baryonic l W ± q u, d e (d) leptonic U(1) L U(2) (Antoniadis, Kiritsis, Rizos, Tomaras; Ibanez, Marchesano, Rabadan; Blumenhagen, Körs, D.L. Ott,...) U(1) R

32 IIA Intersecting branes: Stacks of D6-branes, wrapped around CY 3-cycles: Basis of homology 3-cycles: α I,β I (I =0,...h 2,1 )

33 IIA Intersecting branes: Stacks of D6-branes, wrapped around CY 3-cycles: Basis of homology 3-cycles: α I,β I (I =0,...h 2,1 ) Geometrical input data:

34 IIA Intersecting branes: Stacks of D6-branes, wrapped around CY 3-cycles: Basis of homology 3-cycles: α I,β I (I =0,...h 2,1 ) Geometrical input data: number of D6-branes in each stack (a =1,...,k) N a :

35 IIA Intersecting branes: Stacks of D6-branes, wrapped around CY 3-cycles: Basis of homology 3-cycles: α I,β I (I =0,...h 2,1 ) Geometrical input data: number of D6-branes in each stack N a : (a =1,...,k) X I a,y I a : integer wrapping numbers around α I,β I cycle Π a = X I aα I + Y I a β I

36 IIA Intersecting branes: Stacks of D6-branes, wrapped around CY 3-cycles: Basis of homology 3-cycles: α I,β I (I =0,...h 2,1 ) Geometrical input data: number of D6-branes in each stack N a : (a =1,...,k) X I a,y I a : integer wrapping numbers around α I,β I cycle Π a = X I aα I + Y I Physical output data: Open string 4-dim. gauge group: G = k a=1 a β I U(N a ) 4-dim. massless fermions from open strings at intersection points: N F a,b =Π a Π b = X I ay I a b U(N) chiral matter fields b X I b Y I a

37 IIA intersecting D-branes

38 IIA intersecting D-branes Anomalous U(1) s: U(N a )=SU(N a ) U(1) a The U(1) part is in general massive and anomalous due to B F couplings in the CS action.

39 IIA intersecting D-branes Anomalous U(1) s: U(N a )=SU(N a ) U(1) a The U(1) part is in general massive and anomalous due to B F couplings in the CS action. 3 kind of consistency conditions:

40 IIA intersecting D-branes Anomalous U(1) s: U(N a )=SU(N a ) U(1) a The U(1) part is in general massive and anomalous due to B F couplings in the CS action. 3 kind of consistency conditions: Ramond-Ramond tadpole cancellation: k N a (Π a +Π a) = 4Π O6 a=1 (O6 = orientifold plane)

41 IIA intersecting D-branes Anomalous U(1) s: U(N a )=SU(N a ) U(1) a The U(1) part is in general massive and anomalous due to B F couplings in the CS action. 3 kind of consistency conditions: Ramond-Ramond tadpole cancellation: k N a (Π a +Π a) = 4Π O6 a=1 Supersymmetry condition: (O6 = orientifold plane) J Πa =0, Im(e iθ a Ω Πa )=0

42 IIA intersecting D-branes Anomalous U(1) s: U(N a )=SU(N a ) U(1) a The U(1) part is in general massive and anomalous due to B F couplings in the CS action. 3 kind of consistency conditions: Ramond-Ramond tadpole cancellation: k N a (Π a +Π a) = 4Π O6 a=1 Supersymmetry condition: (O6 = orientifold plane) J Πa =0, Im(e iθ a Ω Πa )=0 K-theory conditions. (A. Uranga)

43 IIA intersecting D-branes Anomalous U(1) s: U(N a )=SU(N a ) U(1) a The U(1) part is in general massive and anomalous due to B F couplings in the CS action. 3 kind of consistency conditions: Ramond-Ramond tadpole cancellation: k N a (Π a +Π a) = 4Π O6 a=1 Supersymmetry condition: (O6 = orientifold plane) J Πa =0, Im(e iθ a Ω Πa )=0 K-theory conditions. (A. Uranga) Large, but finite number of solutions. D-brane statistics! (R. Blumenhagen, F. Gmeiner, G. Honecker, D. L., M. Stein, T. Weigand; M. Douglas, W. Taylor; T. Dijkstra, L. Huiszoon, A. Schellekens)

44 (Intersecting) D-brane statistics How many orientifold models exist which come close to the (spectrum of the) MSSM? (Blumenhagen, Gmeiner, Honecker, Lüst, Stein, Weigand, hep-th/ , hep-th/ , hep-th/ ; related work: Dijkstra, Huiszoon, Schellekens, hep-th/ ; Anastasopoulos, Dijkstra, Kiritsis, Schellekens, hep-th/ ; Douglas, Taylor, hep-th/ ; Dienes, Lennek, hep-th/ ; Rosenhaus, Taylor, arxiv: ) (i) Example: M 6 = T 6 /(Z 2 Z 2 ) IIA orientifold: Systematic computer search (NP complete problem): Look for solutions of a set of diophantic equations: There exist about susy D-brane models on this orbifold (with restricted complex structure)! Finiteness of models was proven by Douglas, Taylor.

45 (Intersecting) D-brane model building Require additional further phenomenological restrictions:

46 (Intersecting) D-brane model building Require additional further phenomenological restrictions: Restriction Factor gauge factor U(3) gauge factor U(2)/Sp(2) No symmetric representations Massless U(1) Y Three generations of quarks Three generations of leptons Total

47 (Intersecting) D-brane model building Require additional further phenomenological restrictions: Restriction Factor gauge factor U(3) gauge factor U(2)/Sp(2) No symmetric representations Massless U(1) Y Three generations of quarks Three generations of leptons Total Only one in a billion models gives rise to a MSSM like vacuum!

48 (Intersecting) D-brane model building Require additional further phenomenological restrictions: Restriction Factor gauge factor U(3) gauge factor U(2)/Sp(2) No symmetric representations Massless U(1) Y Three generations of quarks Three generations of leptons Total Only one in a billion models gives rise to a MSSM like vacuum! Interesting models for large complex structure moduli (Rosenhaus, Taylor).

49 (Intersecting) D-brane model building Require additional further phenomenological restrictions: Restriction Factor gauge factor U(3) gauge factor U(2)/Sp(2) No symmetric representations Massless U(1) Y Three generations of quarks Three generations of leptons Total Only one in a billion models gives rise to a MSSM like vacuum! Interesting models for large complex structure moduli (Rosenhaus, Taylor). However always chiral, massless exotics!

50 (ii) Z6-orientifold: (exceptional, blowing-up 3-cycles!) (Gmeiner, Lüst, Stein, hep-th/ ) In total susy D-brane models of them possess MSSM like spectra!

51 (ii) Z6-orientifold: (exceptional, blowing-up 3-cycles!) In total susy D-brane models of them possess MSSM like spectra! (iii) Z6 -orientifold: (Gmeiner, Lüst, Stein, hep-th/ ) (Gmeiner, Honecker, arxiv: ) Millions of standard models!

52 (ii) Z6-orientifold: (exceptional, blowing-up 3-cycles!) (Gmeiner, Lüst, Stein, hep-th/ ) In total susy D-brane models of them possess MSSM like spectra! (iii) Z6 -orientifold: (Gmeiner, Honecker, arxiv: ) Millions of standard models! models ABa ABb BBa BBb SM gauge group with # of generations gen.

53 (ii) Z6-orientifold: (exceptional, blowing-up 3-cycles!) (Gmeiner, Lüst, Stein, hep-th/ ) In total susy D-brane models of them possess MSSM like spectra! (iii) Z6 -orientifold: (Gmeiner, Honecker, arxiv: ) Millions of standard models! models SM gauge group, 3 generations with # of Higgses h

54 (ii) Z6-orientifold: (exceptional, blowing-up 3-cycles!) In total susy D-brane models of them possess MSSM like spectra! (iii) Z6 -orientifold: (Gmeiner, Lüst, Stein, hep-th/ ) (Gmeiner, Honecker, arxiv: ) Millions of standard models! P(models) SM gauge group, 3 generations with # of chiral exotics!

55 (ii) Z6-orientifold: (exceptional, blowing-up 3-cycles!) In total susy D-brane models of them possess MSSM like spectra! (iii) Z6 -orientifold: (Gmeiner, Lüst, Stein, hep-th/ ) (Gmeiner, Honecker, arxiv: ) Millions of standard models! P(models) ISB models with no chiral exotics are possible! SM gauge group, 3 generations with # of chiral exotics!

56 Problem of realizing other GUT theories in perturbative orientifolds: SO(10) GUT: no spinor (16) representations from open strings No exceptional gauge groups from open strings. Additional problem: SU(5): Some (up or down type) Yukawa couplings are absent in perturbation theory.

57 Non-perturbative D-instantons: (M. Dine, N. Seiberg, X. Wen, E. Witten; K. Becker, M. Becker, A. Strominger; M. Green, M. Gutperle; J. Harvey, G. Moore; M. Billo, M. Frau, F. Fucito, A. Lerda, I. Pesandro; N. Dorey, T. Hollowwod, V. Khoze;... Recent review: M. Bianchi, S. Kovacs, G. Rossi)

58 Non-perturbative D-instantons: (M. Dine, N. Seiberg, X. Wen, E. Witten; K. Becker, M. Becker, A. Strominger; M. Green, M. Gutperle; J. Harvey, G. Moore; M. Billo, M. Frau, F. Fucito, A. Lerda, I. Pesandro; N. Dorey, T. Hollowwod, V. Khoze;... Recent review: M. Bianchi, S. Kovacs, G. Rossi) Perturbative effective action:

59 Non-perturbative D-instantons: (M. Dine, N. Seiberg, X. Wen, E. Witten; K. Becker, M. Becker, A. Strominger; M. Green, M. Gutperle; J. Harvey, G. Moore; M. Billo, M. Frau, F. Fucito, A. Lerda, I. Pesandro; N. Dorey, T. Hollowwod, V. Khoze;... Recent review: M. Bianchi, S. Kovacs, G. Rossi) Perturbative effective action: SM-sector: Contains global U(1) symmetries that forbid certain couplings (neutrino masses, Yukawa couplings)

60 Non-perturbative D-instantons: (M. Dine, N. Seiberg, X. Wen, E. Witten; K. Becker, M. Becker, A. Strominger; M. Green, M. Gutperle; J. Harvey, G. Moore; M. Billo, M. Frau, F. Fucito, A. Lerda, I. Pesandro; N. Dorey, T. Hollowwod, V. Khoze;... Recent review: M. Bianchi, S. Kovacs, G. Rossi) Perturbative effective action: SM-sector: Contains global U(1) symmetries that forbid certain couplings (neutrino masses, Yukawa couplings) Hidden sector: Moduli stabilization by fluxes. Very often, not all moduli are stabilized.

61 Non-perturbative D-instantons: (M. Dine, N. Seiberg, X. Wen, E. Witten; K. Becker, M. Becker, A. Strominger; M. Green, M. Gutperle; J. Harvey, G. Moore; M. Billo, M. Frau, F. Fucito, A. Lerda, I. Pesandro; N. Dorey, T. Hollowwod, V. Khoze;... Recent review: M. Bianchi, S. Kovacs, G. Rossi) Perturbative effective action: SM-sector: Contains global U(1) symmetries that forbid certain couplings (neutrino masses, Yukawa couplings) Hidden sector: Moduli stabilization by fluxes. Very often, not all moduli are stabilized. Unbroken space-time supersymmetry.

62 Non-perturbative D-instantons: (M. Dine, N. Seiberg, X. Wen, E. Witten; K. Becker, M. Becker, A. Strominger; M. Green, M. Gutperle; J. Harvey, G. Moore; M. Billo, M. Frau, F. Fucito, A. Lerda, I. Pesandro; N. Dorey, T. Hollowwod, V. Khoze;... Recent review: M. Bianchi, S. Kovacs, G. Rossi) Perturbative effective action: SM-sector: Contains global U(1) symmetries that forbid certain couplings (neutrino masses, Yukawa couplings) Hidden sector: Moduli stabilization by fluxes. Very often, not all moduli are stabilized. Unbroken space-time supersymmetry. Take into account non-perturbative instanton corrections to the effective action!

63 String instanton corrections:

64 String instanton corrections: String instantons arise in a geometric way from branes wrapped around internal cycles.

65 String instanton corrections: String instantons arise in a geometric way from branes wrapped around internal cycles. It is possible to compute string instanton corrections from open string CFT (not only guess them from field theory).

66 String instanton corrections: String instantons arise in a geometric way from branes wrapped around internal cycles. It is possible to compute string instanton corrections from open string CFT (not only guess them from field theory). String instantons can break axionic shift symmetries and hence global U(1) symmetries.

67 String instanton corrections: String instantons arise in a geometric way from branes wrapped around internal cycles. It is possible to compute string instanton corrections from open string CFT (not only guess them from field theory). String instantons can break axionic shift symmetries and hence global U(1) symmetries. Can generate new moduli dependent terms in the superpotential and hence are important for the moduli stabilization and supersymmetry breaking.

68 String instanton corrections: String instantons arise in a geometric way from branes wrapped around internal cycles. It is possible to compute string instanton corrections from open string CFT (not only guess them from field theory). String instantons can break axionic shift symmetries and hence global U(1) symmetries. Can generate new moduli dependent terms in the superpotential and hence are important for the moduli stabilization and supersymmetry breaking. Can generate new matter couplings (Majorana masses, Yukawa couplings) see in a moment.

69 String instanton corrections: String instantons arise in a geometric way from branes wrapped around internal cycles. It is possible to compute string instanton corrections from open string CFT (not only guess them from field theory). String instantons can break axionic shift symmetries and hence global U(1) symmetries. Can generate new moduli dependent terms in the superpotential and hence are important for the moduli stabilization and supersymmetry breaking. Can generate new matter couplings (Majorana masses, Yukawa couplings) see in a moment. (S. Kachru, R. Kallosh, A. Linde, S. Trivedi (2003);F. Denef, M. Douglas, B. Florea, A. Grassi, S. Kachru (2005); R. Blumenhagen, M. Cvetic, T. Weigand; D.L., S. Reffert, E. Scheidegger, W. Schulgin, S. Stieberger; Ibanez, Uranga (2006)...)

70 Geometry: Non space-time filling Euclidean D- branes:

71 Geometry: Non space-time filling Euclidean D- branes: Two kinds of string instantons:

72 Geometry: Non space-time filling Euclidean D- branes: Two kinds of string instantons: World-sheet instantons: exp( J/α ). Tree-level in CFT!

73 Geometry: Non space-time filling Euclidean D- branes: Two kinds of string instantons: World-sheet instantons: Space-time instantons: exp( 1/g s ) exp( J/α ). Tree-level in CFT!

74 Geometry: Non space-time filling Euclidean D- branes: Two kinds of string instantons: World-sheet instantons: Space-time instantons: exp( 1/g s ) exp( J/α ). Tree-level in CFT! These are non-space time filling D(p)=E(p) branes wrapped around internal (p+1)-cycles:

75 Geometry: Non space-time filling Euclidean D- branes: Two kinds of string instantons: World-sheet instantons: Space-time instantons: exp( 1/g s ) exp( J/α ). Tree-level in CFT! These are non-space time filling D(p)=E(p) branes wrapped around internal (p+1)-cycles: IIA: special lagrangian submanifolds: E2 on 3-cycles Mirror symmetry (SYZ) IIB: points, (complex lines), divisors, (CY) E(-1) (E1) E3 (E5)

76 Non-perturbative Yukawa couplings: (R. Blumenhagen, M. Cvetic, D. Lüst, R. Richter, T. Weigand, arxiv: )

77 Non-perturbative Yukawa couplings: (R. Blumenhagen, M. Cvetic, D. Lüst, R. Richter, T. Weigand, arxiv: ) SU(5) GUT intersecting D6-brane models:

78 Non-perturbative Yukawa couplings: (R. Blumenhagen, M. Cvetic, D. Lüst, R. Richter, T. Weigand, arxiv: ) SU(5) GUT intersecting D6-brane models: Consider two stack a and b of D6-branes: G = U(5) a U(1) b = SU(5) a U(1) a U(1) b Open strings: sector number U(5) a U(1) b reps. U(1) X (a 1,a) 3 + (1, 1) 10 (2,0) 2 (a, b) 3 5 ( 1,1) 3 2 (b 5,b) 3 1 (0, 2) 2 (a,b) 1 5 H (1,1) + 5H ( 1, 1) ( 1) + (1)

79 Non-perturbative Yukawa couplings: (R. Blumenhagen, M. Cvetic, D. Lüst, R. Richter, T. Weigand, arxiv: ) SU(5) GUT intersecting D6-brane models: Consider two stack a and b of D6-branes: G = U(5) a U(1) b = SU(5) a U(1) a U(1) b Open strings: sector number U(5) a U(1) b reps. U(1) X (a 1,a) 3 + (1, 1) 10 (2,0) 2 (a, b) 3 5 ( 1,1) 3 2 (b 5,b) 3 1 (0, 2) 2 (a,b) 1 5 H (1,1) + 5H ( 1, 1) ( 1) + (1) Abelian symmetries: U(1) a U(1) b One anomalous linear combination: global symmetry One anomaly free linear combination U(1) X

80

81 From U(1) X charges it follows that: Perturb. allowed couplings(e.g. u,c,t-quarks): 10 (2,0) 5 ( 1,1) 5 H ( 1, 1), Perturb. forbidden couplings (e.g. d,s,b-quarks): 10 (2,0) 10 (2,0) 5 H (1,1)

82 From U(1) X charges it follows that: Perturb. allowed couplings(e.g. u,c,t-quarks): 10 (2,0) 5 ( 1,1) 5 H ( 1, 1), Perturb. forbidden couplings (e.g. d,s,b-quarks): 10 (2,0) 10 (2,0) 5 H (1,1) These can be generated by E2-instantons: The instanton has to wrap a rigid 3-cycle Ξ invariant under the orientfold projection Ω σ and carrying gauge group O(1)

83 From U(1) X charges it follows that: Perturb. allowed couplings(e.g. u,c,t-quarks): 10 (2,0) 5 ( 1,1) 5 H ( 1, 1), Perturb. forbidden couplings (e.g. d,s,b-quarks): 10 (2,0) 10 (2,0) 5 H (1,1) These can be generated by E2-instantons: The instanton has to wrap a rigid 3-cycle Ξ invariant under the orientfold projection Ω σ and carrying gauge group O(1) ( Talks by Anastasopolous, Blumenhagen)

84 Non-perturbative constructions: (i) IIA orientifolds with intersecting D6-branes M-theory on 7-dim. G2 manifolds (Acharya, Atiyah, Witten,...) Gauge bosons live on 3-dimensional singularities Q3 D6-branes Chiral fermions live on 0-dimensional conical singularities (points on 7-dim manifolds) Intersections of D6-branes Local ALE fibrations over Q3 were recently constructed: Pantev, Wijnholt, arxiv:

85 (ii) IIB orientifolds with intersecting D7-branes F-theory on 8-dim. CY 4-folds (GUT models) (Beasly, Heckman, Vafa; Donagi, Wijnholt,...) Local set up: Gauge bosons live on 4-dimensional ADE-singularities D7-branes Chiral fermions live on 2-dimensional singularities Intersections of D7-branes

86 (ii) IIB orientifolds with intersecting D7-branes F-theory on 8-dim. CY 4-folds (GUT models) (Beasly, Heckman, Vafa; Donagi, Wijnholt,...) Local set up: Gauge bosons live on 4-dimensional ADE-singularities D7-branes Chiral fermions live on 2-dimensional singularities Intersections of D7-branes F-theory models contain several non-perturbative features: exceptional gauge groups matter in spinor representations non zero Yukawa coupl. (intersections of 3 matter curves)

87 (ii) IIB orientifolds with intersecting D7-branes F-theory on 8-dim. CY 4-folds (GUT models) (Beasly, Heckman, Vafa; Donagi, Wijnholt,...) Local set up: Gauge bosons live on 4-dimensional ADE-singularities D7-branes Chiral fermions live on 2-dimensional singularities Intersections of D7-branes F-theory models contain several non-perturbative features: exceptional gauge groups matter in spinor representations non zero Yukawa coupl. (intersections of 3 matter curves) Global models: Blumenhagen, Grimm, Jurke, Weigand, arxiv: , arxiv: ; Marsano, Saulina, Schafer-Nameki, arxiv: , arxiv:

88 (ii) IIB orientifolds with intersecting D7-branes F-theory on 8-dim. CY 4-folds (GUT models) (Beasly, Heckman, Vafa; Donagi, Wijnholt,...) Local set up: Gauge bosons live on 4-dimensional ADE-singularities D7-branes Chiral fermions live on 2-dimensional singularities Intersections of D7-branes F-theory models contain several non-perturbative features: exceptional gauge groups matter in spinor representations non zero Yukawa coupl. (intersections of 3 matter curves) Global models: Blumenhagen, Grimm, Jurke, Weigand, arxiv: , arxiv: ; Marsano, Saulina, Schafer-Nameki, arxiv: , arxiv: ( Talks by Blumenhagen, Klemm, Tatar, Wijnholt)

89 Outline Intersecting D-brane models (Lecture I) Stringy signatures at LHC (The LHC string hunter s companion) (Lecture II) (D. Lüst, S. Stieberger, T. Taylor, arxiv: ; L. Anchordoqui, H. Goldberg, D. Lüst, S. Nawata, S. Stieberger, T. Taylor, arxiv: [hep-ph]; arxiv: [hep-ph] D. Lüst, O. Schlotterer, S. Stieberger, T. Taylor, arxiv: )

90 Outline Intersecting D-brane models (Lecture I) Stringy signatures at LHC (The LHC string hunter s companion) (Lecture II) (D. Lüst, S. Stieberger, T. Taylor, arxiv: ; L. Anchordoqui, H. Goldberg, D. Lüst, S. Nawata, S. Stieberger, T. Taylor, arxiv: [hep-ph]; arxiv: [hep-ph] D. Lüst, O. Schlotterer, S. Stieberger, T. Taylor, arxiv: ) ( Talk by Antoniadis)

91 II) The LHC String Hunter s Companion: Recall basic set-up of type IIA/B orientifolds: Gravitons live as closed strings in 10-dimensional bulk. Non-Abelian gauge bosons live as open strings on lower dimensional D-branes. Chiral fermions are open strings on the intersection locus of two D-branes:

92 3 basic assumptions:

93 3 basic assumptions: (i) Consider orientifold compact. which realize the SM, i.e. contain the SM D-brane quiver:

94 3 basic assumptions: (a) baryonic q (i) Consider orientifold compact. which realize the SM, W i.e. contain the SM D-brane quiver: ± l (d) leptonic (b) left g u, d (c) right e U(3) U(1) U(2) U(1) R

95 3 basic assumptions: (a) baryonic q (i) Consider orientifold compact. which realize the SM, W i.e. contain the SM D-brane quiver: ± l (d) leptonic U(2) U(1) R (ii) Consider orientifold compactifications which allow for low string scale (solve hierarchy problem without SUSY) Low scale for quantum gravity & large extra dimensions. (b) left g u, d (c) right e U(3) U(1)

96 3 basic assumptions: (a) baryonic q (i) Consider orientifold compact. which realize the SM, W i.e. contain the SM D-brane quiver: ± l (d) leptonic U(2) U(1) R (ii) Consider orientifold compactifications which allow for low string scale (solve hierarchy problem without SUSY) Low scale for quantum gravity & large extra dimensions. (iii) Perturbation theory is valid, i.e. small string coupling. (b) left g u, d (c) right e U(3) U(1)

97 3 basic assumptions: (a) baryonic q (i) Consider orientifold compact. which realize the SM, W i.e. contain the SM D-brane quiver: ± l (d) leptonic U(2) U(1) R (ii) Consider orientifold compactifications which allow for low string scale (solve hierarchy problem without SUSY) Low scale for quantum gravity & large extra dimensions. (iii) Perturbation theory is valid, i.e. small string coupling. (iv) Longitudinal space along D-branes is un-warped. (Discussion of warped case: Perelstein, Spray, arxiv: ) (b) left g u, d (c) right e U(3) U(1)

98 3 basic assumptions: (a) baryonic q (i) Consider orientifold compact. which realize the SM, W i.e. contain the SM D-brane quiver: ± l (d) leptonic U(2) U(1) R (ii) Consider orientifold compactifications which allow for low string scale (solve hierarchy problem without SUSY) Low scale for quantum gravity & large extra dimensions. (iii) Perturbation theory is valid, i.e. small string coupling. (iv) Longitudinal space along D-branes is un-warped. (Discussion of warped case: Perelstein, Spray, arxiv: ) Universal predictions that are true for all points in the landscape, i.e. independent from any details of the compact space! (b) left g u, d (c) right e U(3) U(1)

99 Mass scales in D-brane models:

100 Mass scales in D-brane models: There are 3 basic mass scales in D-brane compactifications:

101 Mass scales in D-brane models: There are 3 basic mass scales in D-brane compactifications: String scale: (1) : M s = 1 α

102 Mass scales in D-brane models: There are 3 basic mass scales in D-brane compactifications: String scale: Compatification scale: (1) : M s = 1 α (2) : M 6 = 1 V 1/6 6

103 Mass scales in D-brane models: There are 3 basic mass scales in D-brane compactifications: String scale: (1) : M s = 1 α Compatification scale: (2) : M 6 = 1 V 1/6 6 Scale of wrapped D(p+3)-branes (e.g. IIB: p=0,4), (IIA: p=3): (3) : M p = 1 (V p ) 1/p, (3 ): M 6 p = V 6 = V p V 6 p 1 (V 6 p )1/(6 p)

104 There are 2 basic 4D observables:

105 There are 2 basic 4D observables: Strength of 4D gravitational interactions: (A) : M 2 Planck M 8 s V GeV

106 There are 2 basic 4D observables: Strength of 4D gravitational interactions: (A) : M 2 Planck M 8 s V GeV Strength of 4D gauge interactions: (B) : g 2 Dp M s p V p O(1) = (V p ) 1/p M s

107 There are 2 basic 4D observables: Strength of 4D gravitational interactions: (A) : M 2 Planck M 8 s V GeV Strength of 4D gauge interactions: (B) : g 2 Dp M s p V p O(1) = (V p ) 1/p M s (A) and (B): leave one free parameter. M s is a free parameter in D-brane compactifications!

108 There are 4 natural scenarios for the string scale:

109 There are 4 natural scenarios for the string scale: (o) Planck scale scenario: M s is the gravitational 4D Planck scale M s M Planck GeV Gauge coupling unification at the Planck scales needs further effects (string threshold corrections,...)

110 Alternatively relate the string scale to particles physics mass scales. (i) GUT scale scenario: M s is the 4D scale of gauge coupling unification M s M GUT GeV ( M GUT = M SM exp ) g 2 Dp (M SM) g 2 Dp (M GUT ) b p

111 Alternatively relate the string scale to particles physics mass scales. (i) GUT scale scenario: M s is the 4D scale of gauge coupling unification M s M GUT GeV ( M GUT = M SM exp ) g 2 Dp (M SM) g 2 Dp (M GUT ) b p Recent GUT string model building in F-theory and IIB orientifolds: (Beasly, Heckman, Marsano, Saulina, Schafer-Nameki, Vafa; Donagi, Wijnholt; Blumenhagen, Braun, Grimm, Weigand) D7-branes wrapped on del Pezzo surfaces GUT gauge group is broken by U(1) Y flux

112 (ii) SUSY breaking scenario: M s is the intermediate 4D scale of supersymmetry breaking (Balasubramanian, Conlon, Quevedo, Suruliz,...) M s M SUSY GeV Gravity mediation: M SUSY M SM M Planck (No natural gauge coupling unification!)

113 (iii) Low string scale scenario: (Antoniadis, Arkani-Hamed, Dimopoulos, Dvali) M s is the Standard Model (TeV) scale: M s M SM 10 3 GeV (No natural gauge coupling unification!) (Effective scale of gravity is high (i.e. gravity is weak), since the gravitons can propagate into the large 6- dim. bulk space!) Dimensionless volumes in string units, corresponding to the four scenarios: V 6 = V 6 M 6 s = M 2 Planck M 2 s =1, 10 6, 10 16, 10 32

114 There are 4 generic types of particles:

115 There are 4 generic types of particles: (i) Stringy Regge excitations: M Regge = nm s = n V M Planck, (n =1,..., ) 6 Open string excitations: completely universal (model independent), carry SM gauge quantum numbers: higher spin excitations of g,w,z,γ, q, l

116 (ii) D-brane cycle Kaluza Klein excitations: M KK = m (V p ) mm 1/p s = m M Planck (V 6 (m =1,..., ) )1/2 Open strings, depend on the details of the internal geometry, carry SM gauge quantum numbers Internal momenta excitations of g, W, Z, γ, q, l

117 (ii) D-brane cycle Kaluza Klein excitations: M KK = m (V p ) mm 1/p s = m M Planck (V 6 (m =1,..., ) )1/2 Open strings, depend on the details of the internal geometry, carry SM gauge quantum numbers Internal momenta excitations of g, W, Z, γ, q, l The string Regge excitations and the D-brane cycle KK modes are charged under the SM and have mass of order M s can they be seen at LHC?!

118 (iii) Overall volume modulus: M T = M Planck (V 6 )3/2 = 1019, 10 10, 10 5, GeV Closed string, model independent, neutral under the SM, interacts only gravitationally Problem: the very light mass causes a fifth force. Would rule out TeV string scale!

119 (iii) Overall volume modulus: M T = M Planck (V 6 )3/2 = 1019, 10 10, 10 5, GeV Closed string, model independent, neutral under the SM, interacts only gravitationally Problem: the very light mass causes a fifth force. Would rule out TeV string scale!

120 (iii) Overall volume modulus: M T = M Planck (V 6 )3/2 = 1019, 10 10, 10 5, GeV Closed string, model independent, neutral under the SM, interacts only gravitationally Problem: the very light mass causes a fifth force. Would rule out TeV string scale! But one expects a mass shift by radiative corrections: (G. Dvali, D. Lüst, work in progress) M T <Tµ µ T µ µ > M 2 Planck M 4 s M 2 Planck GeV

121 (iv) Mini black holes (string balls): These are non-perturbative states, associated to the higher dimensional gravity scale: M b.h. = M s g 2 s >> M s if g s < 1 Weakly coupled string theory: gravity effects occur much above! M s Regge excitations: M Regge M s n If g s =0.1 = n =1/g 4 s 10 4 string states before one reaches black hole!

122 Type IIB orientifolds: Realization of low string scale compatifications on Swiss Cheese Manifolds: (Abdussalam, Allanach, Balasubramanian, Berglund, Cicoli, Conlon, Kom, Quevedo, Suruliz; Blumenhagen, Moster, Plauschinn; for model building and phenomenological aspects see: Conlon, Maharana, Quevedo, arxiv: )

123 Type IIB orientifolds: Realization of low string scale compatifications on Swiss Cheese Manifolds: (Abdussalam, Allanach, Balasubramanian, Berglund, Cicoli, Conlon, Kom, Quevedo, Suruliz; Blumenhagen, Moster, Plauschinn; for model building and phenomenological aspects see: Conlon, Maharana, Quevedo, arxiv: ) BULK U(3) Q L Q R BLOW!UP U(2) U(1) e L e R U(1) 2 requirements: - Negative Euler number. - SM lives on D7-branes around small cycles of the CY. One needs at least one blow-up mode (resolves point like singularity).

124 Type IIB orientifolds: Realization of low string scale compatifications on Swiss Cheese Manifolds: (Abdussalam, Allanach, Balasubramanian, Berglund, Cicoli, Conlon, Kom, Quevedo, Suruliz; Blumenhagen, Moster, Plauschinn; for model building and phenomenological aspects see: Conlon, Maharana, Quevedo, arxiv: ) BULK Moduli potential: U(3) Q L Q R BLOW!UP Kähler potential: K = K cs 2 log U(2) U(1) e L e R U(1) 2 requirements: - Negative Euler number. - SM lives on D7-branes around small cycles of the CY. One needs at least one blow-up mode (resolves point like singularity). ( V 6 + ξ 2g 3 2 s Superpotential: W = W cs + A i exp( a i t i ) Moduli stabilization Minima: Large hierarchical scales with V 6 Ms 6 = 10 16, ) (Becker,Becker, Haack, Louis)

125 In general: Consider a theory with N species of particles with mass M: (G. Dvali, arxiv: ; G. Dvali, D. Lüst, arxiv: ) Bounds from black hole decays: N < N max = M 2 P lanck M 2 M: scale of new physics (A quantum black hole can emit at most N max different particles) This bound must be satisfied in every effective string vacuum that is consistently coupled to gravity! E.g. if a scalar field in the effective potential gives mass to N particles via the Higgs effect: M = M(φ) M(φ) 2 < M 2 P lanck N Bound forbids essentially large trans-planckian vevs:

126 E.g: N = = M<10 16 M P lanck 1 T ev This bound gives also a possible explanation of the hierarchy problem: M can be seen as the fundamental scale of gravity, which is diluted by the presence on the N particle species.

127 E.g: N = = M<10 16 M P lanck 1 T ev This bound gives also a possible explanation of the hierarchy problem: M can be seen as the fundamental scale of gravity, which is diluted by the presence on the N particle species. dramatic effects at the LHC.

128 E.g: N = = M<10 16 M P lanck 1 T ev This bound gives also a possible explanation of the hierarchy problem: M can be seen as the fundamental scale of gravity, which is diluted by the presence on the N particle species. dramatic effects at the LHC. Is there a stringy realization of the large N species scenario? (G. Dvali, D. Lüst, work in progress)

129 Test of D-brane models at the LHC: gg, qq,, qg X g, γ, Z, W, q, l In string perturbation theory production of:

130 Test of D-brane models at the LHC: gg, qq,, qg X g, γ, Z, W, q, l In string perturbation theory production of: - Regge excitations of higher spin: First resonances: g q spin 0,1,2 & spin 1/2, 3/2

131 Test of D-brane models at the LHC: gg, qq,, qg X g, γ, Z, W, q, l In string perturbation theory production of: - Regge excitations of higher spin: First resonances: g q spin 0,1,2 & spin 1/2, 3/2 - Kaluza Klein (KK) (and winding) modes

132 Test of D-brane models at the LHC: gg, qq,, qg X g, γ, Z, W, q, l In string perturbation theory production of: - Regge excitations of higher spin: First resonances: g q spin 0,1,2 & spin 1/2, 3/2 - Kaluza Klein (KK) (and winding) modes (- Z gauge bosons, black holes)

133 Test of D-brane models at the LHC: gg, qq,, qg X g, γ, Z, W, q, l In string perturbation theory production of: - Regge excitations of higher spin: First resonances: g spin 0,1,2 & spin 1/2, 3/2 - Kaluza Klein (KK) (and winding) modes (- Z gauge bosons, black holes) One has to compute the parton model cross sections of SM fields into new stringy states! q

134 The string scattering amplitudes exhibit some interesting properties: Interesting mathematical structure They go beyond the N=4 Yang-Mills amplitudes: (i) The contain quarks & leptons in fundamental repr. Quark, lepton vertex operators: V q,l (z, u, k) =u α S α (z)ξ a b (z)e φ(z)/2 e ik X(z) Fermions: boundary changing (twist) operators! Striking relation between quark and gluon amplitudes! (ii) They contain stringy corrections.

135 n-point tree amplitudes with 0 or 2 open string fermions (quarks, leptons) and N or N-2 gauge bosons (gluons) are completely model independent. Information about the string Regge spectrum. KK modes are seen in scattering processes with more than 2 fermions. Information about the internal geometry. g N g N q 1 g N 1 q 1 g N 1 g KK g 5 q 2 g 4 q 2 q 4 g 3 q 3

136 Parton model cross sections of SM-fields:

137 Parton model cross sections of SM-fields: Disk amplitude n among external SM fields (q, l, g, γ,z 0,W ± ) : e.g. n=4: A(Φ 1, Φ 2, Φ 3, Φ 4 )=<V Φ 1(z 1 ) V Φ 2(z 2 ) V Φ 3(z 3 ) V Φ 4(z 4 ) > disk

138 Parton model cross sections of SM-fields: Disk amplitude n among external SM fields (q, l, g, γ,z 0,W ± ) : e.g. n=4: A(Φ 1, Φ 2, Φ 3, Φ 4 )=<V Φ 1(z 1 ) V Φ 2(z 2 ) V Φ 3(z 3 ) V Φ 4(z 4 ) > disk (b) left g (c) right U(3) (a) baryonic q u, d W ± l e (d) leptonic U(1) L U(2) U(1) R

139 Parton model cross sections of SM-fields: Disk amplitude n among external SM fields (q, l, g, γ,z 0,W ± ) : e.g. n=4: A(Φ 1, Φ 2, Φ 3, Φ 4 )=<V Φ 1(z 1 ) V Φ 2(z 2 ) V Φ 3(z 3 ) V Φ 4(z 4 ) > disk These amplitudes are dominated by the following poles:

140 Parton model cross sections of SM-fields: Disk amplitude n among external SM fields (q, l, g, γ,z 0,W ± ) : e.g. n=4: These amplitudes are dominated by the following poles: Exchange of SM fields A(Φ 1, Φ 2, Φ 3, Φ 4 )=<V Φ 1(z 1 ) V Φ 2(z 2 ) V Φ 3(z 3 ) V Φ 4(z 4 ) > disk

141 Parton model cross sections of SM-fields: Disk amplitude n among external SM fields (q, l, g, γ,z 0,W ± ) : e.g. n=4: These amplitudes are dominated by the following poles: Exchange of SM fields Exchange of string Regge resonances (Veneziano like ampl.) new contact interactions: k 1 k 2 A(Φ 1, Φ 2, Φ 3, Φ 4 )=<V Φ 1(z 1 ) V Φ 2(z 2 ) V Φ 3(z 3 ) V Φ 4(z 4 ) > disk k; n A(k 1,k 2,k 3,k 4 ; α ) Γ( α s) Γ(1 α u) Γ( α s α u) k 3 = k 4 n=0 γ(n) s M 2 n α 2 α 2 ζ(2) trf 4 t s π2 6 tu (α ) V s (α )= Γ(1 s/m string 2 )Γ(1 u/m string 2 ) Γ(1 t/mstring 2 ) =1 π2 6 M 4 6 stringsu ζ(3)mstring stu + 1 α 0

142 Parton model cross sections of SM-fields: Disk amplitude n among external SM fields (q, l, g, γ,z 0,W ± ) : e.g. n=4: These amplitudes are dominated by the following poles: Exchange of SM fields Exchange of string Regge resonances (Veneziano like ampl.) new contact interactions: k 1 k 2 A(Φ 1, Φ 2, Φ 3, Φ 4 )=<V Φ 1(z 1 ) V Φ 2(z 2 ) V Φ 3(z 3 ) V Φ 4(z 4 ) > disk k; n A(k 1,k 2,k 3,k 4 ; α ) Γ( α s) Γ(1 α u) Γ( α s α u) Exchange of KK and winding modes (model dependent) k 3 = k 4 n=0 γ(n) s M 2 n α 2 α 2 ζ(2) trf 4 t s π2 6 tu (α ) V s (α )= Γ(1 s/m string 2 )Γ(1 u/m string 2 ) Γ(1 t/mstring 2 ) =1 π2 6 M 4 6 stringsu ζ(3)mstring stu + 1 α 0

143 4 gauge boson amplitudes: a z 2 z 3 A a 2 A a 3 Disk amplitude: a a z 1 A a 1 A a 4 z 4 a

144 4 gauge boson amplitudes: a z 2 z 3 A a 2 A a 3 Disk amplitude: a a z 1 A a 1 A a 4 z 4 Only string Regge resonances are exchanged These amplitudes are completely model independent! a

145 4 gauge boson amplitudes: a z 2 z 3 A a 2 A a 3 Disk amplitude: a a z 1 A a 1 A a 4 z 4 Only string Regge resonances are exchanged These amplitudes are completely model independent! Examples: a

146 4 gauge boson amplitudes: a z 2 z 3 A a 2 A a 3 Disk amplitude: a a z 1 A a 1 A a 4 z 4 Only string Regge resonances are exchanged These amplitudes are completely model independent! Examples: M(gg gg) 2 = g 4 3 (Stieberger, Taylor) M(gg gγ(z 0 )) 2 = g 4 3 Observable at LHC for M string = 3 TeV a ( 1 s t ) [ 9 u 2 4 s2 Vs 2 (α ) 1 ] 3 ( sv s(α )) 2 +(s t)+(s u) 5 ( 1 6 Q2 A s t ) u 2 dijet events ( sv s (α )+tv t (α )+uv u (α )) 2 (Anchordoqui,Goldberg, Nawata, Taylor, arxiv: )

147 4 gauge boson amplitudes: a z 2 z 3 A a 2 A a 3 Disk amplitude: a a z 1 A a 1 A a 4 z 4 Only string Regge resonances are exchanged These amplitudes are completely model independent! Examples: α 0: M(gg gg) 2 α 0 a agreement with SM! ( 1 s t u 2 ) 9 4( s 2 + t 2 + u 2 ) M(gg γ(z 0 )) 2 α 0 0

148 2 gauge boson - two fermion amplitude: z 2 A a a ψ α 3 β 3 z 3 a z 3 ψ α 3 β 3 b Note: Cullen, Perelstein, Peskin (2000) considered: e + e γγ a b A a A b z 1 z 2 z 1 A a ψ β 4 α 4 z 4 a ψ β 4 α 4 b a z 4 Only string Regge resonances are exchanged These amplitudes are completely model independent! M(qg qg) 2 = g 4 3 s 2 + u 2 t 2 [ V s (α )V u (α ) 4 9 M(qg qγ(z 0 )) 2 = 1 3 g4 3Q 2 A s 2 + u 2 ] 1 su (sv s(α )+uv u (α )) 2 dijet events sut 2 (sv s (α )+uv u (α )) 2

149 2 gauge boson - two fermion amplitude: z 2 A a a ψ α 3 β 3 z 3 a z 3 ψ α 3 β 3 b Note: Cullen, Perelstein, Peskin (2000) considered: e + e γγ a b A a A b z 1 z 2 z 1 A a ψ β 4 α 4 z 4 a ψ β 4 α 4 b a z 4 Only string Regge resonances are exchanged These amplitudes are completely model independent! α 0: agreement with SM! M(qg qg) 2 α 0 = g 4 3 s 2 + u 2 t 2 [ (s + u)2 su M(qg qγ(z 0 )) 2 α 0 = 1 3 g4 3Q 2 s 2 + u 2 A sut 2 (s + u) 2 ]

150 These stringy corrections can be seen in dijet events at LHC: (Anchordoqui, Goldberg, Lüst, Nawata, Stieberger, Taylor, arxiv: [hep-ph]) M Regge = 2 TeV Γ Regge = GeV Widths can be computed in a model independent way! (Anchordoqui, Goldberg, Taylor, arxiv: )

151 These stringy corrections can be seen in dijet events at LHC: (Anchordoqui, Goldberg, Lüst, Nawata, Stieberger, Taylor, arxiv: [hep-ph]) M Regge = 2 TeV Γ Regge = GeV Widths can be computed in a model independent way! (Anchordoqui, Goldberg, Taylor, arxiv: )

152 (see: L. Anchordoqui, H. Goldberg, D. Lüst, S. Nawata, S. Stieberger, T. Taylor, arxiv: [hep-ph]) X 3 X 4 4 fermion amplitudes: z 3 z 2 ψ δ 3 θ γ 3 3 ψ β 2 δ 2 θ 2 Exchange of Regge, KK and winding resonances. These amplitudes are more model dependent and test the internal CY geometry. Constrained by FCNC s M(qq qq) 2 = 2 9 c θ 4 θ 3 ψ δ 3 γ 3 ψ γ 4 α 4 d a ψ β 2 δ 2 θ 2 X 2 ψ α 1 β 1 θ 1 b X X 1 c z 4 θ 4 ψ γ 4 α 4 d d a ψ α 1 β 1 (Abel, Lebedev, Santiago, hep-th/ ) 1 t 2 [ (sf bb tu(α ) ) 2 + ( sf cc tu (α ) ) 2 + ( ug bc ts (α ) ) 2 + ( ug cb + ( sf cc ut (α ) ) 2 + ( tg bc us (α ) ) 2 + ( tg cb us(α ) ) 2 ] 4 27 depend on internal geometry b z 1 θ 1 z 1 u 2 [ (sf bb ut(α ) ) 2 ts(α ) ) ] s 2 tu F bb tu (α )Fut(α bb )+Ftu cc (α )Fut cc (α ) )

153 (see: L. Anchordoqui, H. Goldberg, D. Lüst, S. Nawata, S. Stieberger, T. Taylor, arxiv: [hep-ph]) X 3 c X 4 θ 4 θ 3 4 fermion amplitudes: ψ δ 3 γ 3 ψ γ 4 α 4 d a ψ β 2 δ 2 θ 2 X 2 ψ α 1 β 1 z 3 z 2 ψ δ 3 θ γ 3 3 ψ β 2 δ 2 θ 2 Exchange of Regge, KK and winding resonances. These amplitudes are more model dependent and test the internal CY geometry. Constrained by FCNC s θ 1 b X X 1 c z 4 θ 4 ψ γ 4 α 4 d d a ψ α 1 β 1 (Abel, Lebedev, Santiago, hep-th/ ) b z 1 θ 1 z α 0: agreement with SM! M(qq qq) 2 α 0 4 [ s 2 + u 2 ] 9 t [ s 2 + t 2 ] 9 u s 2 tu

154 KK modes are seen in scattering processes with more than 2 fermions. A(qq qq) 2 = 2 9 (L. Anchordoqui, H. Goldberg, D. Lüst, S. Nawata, S. Stieberger, T. Taylor, arxiv: [hep-ph]) Squared 4-quark amplitude with identical flavors: 1 t 2 [ (sf bb tu(α ) ) 2 + ( sf cc tu (α ) ) 2 + ( ug bc ts (α ) ) 2 + ( ug cb + ( sf cc ut (α ) ) 2 + ( tg bc us (α ) ) 2 + ( tg cb us(α ) ) 2 ] u 2 [ (sf bb ut(α ) ) 2 ts(α ) ) ] s 2 tu F bb tu (α )Fut(α bb )+Ftu cc (α )Fut cc (α ) ) Squared 4-quark amplitude with different flavors: A(qq qq ) 2 = t 2 [ (sf bb tu(α ) ) 2 + ( s Gcc tu (α ) ) 2 + ( ug bc ts (α ) ) 2 + ( ug bc ts (α ) ) 2 ]

155 Dominant contribution: F bb tu = 1 + g2 b t g 2 au + g2 b t g 2 a N p u M 2 ab G bc tu = G bc tu =1 M 2 ab =(M (b) KK )2 +(M (a) wind. )2, e M 2 ab /M 2 s M ab : KK of SU(2) branes and winding modes of SU(3) branes: N p : Degeneracy of KK-states; take N p =3 : Thickness of D-branes M ab =0.7M s

156 Dijet angular contribution by t-channel exchange: CMS detector simulation: Luminosity 1fb 1 10fb 1

157 Five point scattering amplitudes (3 jet events): (Computation of higher point amplitudes for LHC: D. Lüst, O. Schlotterer, S. Stieberger, T. Taylor, arxiv: ). z 2 a a (i) 5 gluons: z 1 A a 2 A a 1 A a 3 z 3 Field theory factors: (Stieberger, Taylor (2006)) a z 5 A a 5 a A a 4 a z 4 M (5) YM = 4g3 YM A(g 1,g 2,g+ 3,g+ 4,g+ 5 )=( V (5) (α,k i ) 2iɛ(1, 2, 3, 4)P (5) (α,k i ) ) M (5) YM z 2 a a (ii) 3 gluons, 2 quarks: z 1 a A a 2 A a 1 A a 3 z 3 a N (5) YM = 4g3 YM β ψ 5 α 5 ψ α 4 β 4 z 5 z 4 b A(g 1,g+ 2,g+ 3,q 4, q+ 5 )=( V (5) (α,k i ) 2iɛ(1, 2, 3, 4)P (5) (α,k i ) ) N (5) YM

158 Five point scattering amplitudes (3 jet events): (i) 5 gluons: (Stieberger, Taylor (2006)) z 1 a a z 5 A a 5 (Computation of higher point amplitudes for LHC: D. Lüst, O. Schlotterer, S. Stieberger, T. Taylor, arxiv: ). z 2 A a 2 A a 1 A a 3 a a A a 4 z 3 a z 4 Field theory factors: M (5) YM = 4g3 YM A(g 1,g 2,g+ 3,g+ 4,g+ 5 ) α 0 M (5) YM, ( V (5) = 1 + ζ(2)o(α 2 ),P (5) = ζ(2)o(α 2 ) ) (ii) 3 gluons, 2 quarks: z 1 a a β ψ 5 α 5 z 2 A a 2 a A a 1 A a 3 ψ α 4 β 4 z 3 a N (5) YM = 4g3 YM z 5 z 4 b A(g 1,g+ 2,g+ 3,q 4, q+ 5 )=( V (5) (α,k i ) 2iɛ(1, 2, 3, 4)P (5) (α,k i ) ) N (5) YM

159 Five point scattering amplitudes (3 jet events): (i) 5 gluons: (Stieberger, Taylor (2006)) z 1 a a z 5 A a 5 (Computation of higher point amplitudes for LHC: D. Lüst, O. Schlotterer, S. Stieberger, T. Taylor, arxiv: ). z 2 A a 2 A a 1 A a 3 a a A a 4 z 3 a z 4 Field theory factors: M (5) YM = 4g3 YM A(g 1,g 2,g+ 3,g+ 4,g+ 5 ) α 0 M (5) YM, ( V (5) = 1 + ζ(2)o(α 2 ),P (5) = ζ(2)o(α 2 ) ) (ii) 3 gluons, 2 quarks: z 1 a a β ψ 5 α 5 z 2 A a 2 a A a 1 A a 3 ψ α 4 β 4 z 3 a N (5) YM = 4g3 YM z 5 z 4 A(g 1,g+ 2,g+ 3,q 4, q+ 5 ) α 0 N (5) b YM

160 The two kinds of amplitudes are universal: the same Regge states are exchanged: k 3 k 3 k 4 k 2 k 4 k; n k ; n k 2 k; n k 1 k 5 k 1 k 5

161 (iii)1 gluon, 4 quarks: z 5 a z 1 A a a ψ γ 5 α 5 ψ α 2 β 2 z 2 c b ψ δ4 γ 4 ψ β 3 δ 3 z 4 z 3 d (1, 2, 3, 4, 5) This amplitude has a similar structure as the 4 quark amplitude: exchange of Regge and KK modes. Factorization on the 4 quark amplitude: A a ψ α 4 β 4 ψ β 5 α 5 ψ β 3 α 3 ψ α 2 β 2 Factorization on the 2 quark - 2 gluon amplitude: ψ β 3 α 3 ψ α 4 β 4 ψ β 5 α 5 ψ α 2 β 2 A a

162 Conclusions

163 Conclusions There exists many ISB models with SM like spectra without chiral exotics.

164 Conclusions There exists many ISB models with SM like spectra without chiral exotics. One can make some model independent predictions: (Independent of amount of (unbroken) supersymmetry!) String tree level, 4-point processes with 2 or 4 gluons observable at LHC?? - M string??

165 Conclusions There exists many ISB models with SM like spectra without chiral exotics. One can make some model independent predictions: (Independent of amount of (unbroken) supersymmetry!) String tree level, 4-point processes with 2 or 4 gluons observable at LHC?? - M string?? Computations done at weak string coupling! Black holes are heavier than Regge states:

166 Conclusions There exists many ISB models with SM like spectra without chiral exotics. One can make some model independent predictions: (Independent of amount of (unbroken) supersymmetry!) String tree level, 4-point processes with 2 or 4 gluons observable at LHC?? - M string?? Computations done at weak string coupling! Black holes are heavier than Regge states: Question: do loop and non-perturbative corrections change tree level signatures? Onset of n.p. physics: M b.h.

167 If nature choses weakly coupled strings with a string scale at a few TeV, LHC should find them!