String Phenomenology ???

Transcription

1 String Phenomenology Andre Lukas Oxford, Theoretical Physics d=11 SUGRA IIB M IIA??? I E x E 8 8 SO(32)

2 Outline A (very) basic introduction to string theory String theory and the real world? Recent work Conclusion

3 String theory

4 String theory Warm-up: world-line of a relativistic particle

5 String theory Warm-up: world-line of a relativistic particle X µ = X µ (τ)

6 String theory Warm-up: world-line of a relativistic particle X µ = X µ (τ) World-line action : S = m dτ dxµ dτ dx ν dτ η µν d 2 X µ dτ 2 = 0

7 World-sheet of free relativistic string

8 World-sheet of free relativistic string X µ = X µ (τ, σ) open string closed string

9 World-sheet of free relativistic string X µ = X µ (τ, σ) open string closed string World-sheet action: S = 1 2πl 2 S d 2 σ det ( X µ σ α X ν σ β η µν )

10 World-sheet of free relativistic string X µ = X µ (τ, σ) open string closed string World-sheet action: string tension, string length S = 1 2πl 2 S d 2 σ det ( X µ σ α l S X ν σ β η µν )

11 World-sheet of free relativistic string X µ = X µ (τ, σ) open string closed string World-sheet action: string tension, string length S = 1 2πl 2 S d 2 σ det ( X µ σ α l S X ν σ β η µν ) Spectrum: l 2 SM = n N n (+ N n )

12 World-sheet of free relativistic string X µ = X µ (τ, σ) open string closed string World-sheet action: string tension, string length S = 1 2πl 2 S d 2 σ det ( X µ σ α l S X ν σ β η µν ) Spectrum: l 2 SM = n N n (+ N n ) Z where N n = α µ nα µ n

13 World-sheet of free relativistic string X µ = X µ (τ, σ) open string closed string World-sheet action: string tension, string length S = 1 2πl 2 S d 2 σ open string det ( X µ σ α l S X ν σ β η µν ) Spectrum: l 2 SM = n N n (+ N n ) Z where N n = α µ nα µ n

14 World-sheet of free relativistic string X µ = X µ (τ, σ) open string closed string World-sheet action: string tension, string length S = 1 2πl 2 S d 2 σ open string det ( X µ σ α l S X ν σ β η µν ) Spectrum: l 2 SM = n N n (+ N n ) Z where N n = α µ nα µ n closed string

15 World-sheet of free relativistic string X µ = X µ (τ, σ) open string closed string World-sheet action: string tension, string length S = 1 2πl 2 S d 2 σ open string det ( X µ σ α l S X ν σ β η µν ) Spectrum: l 2 SM = n N n (+ N n ) closed string

16 World-sheet of free relativistic string X µ = X µ (τ, σ) open string closed string World-sheet action: string tension, string length S = 1 2πl 2 S d 2 σ det ( X µ σ α l S X ν σ β η µν ) open string Spectrum: lsm 2 = N n (+ N n ) = n closed string { 0 observed 1 massive

17 Lowest string states

18 Lowest string states open string: α µ 0 > 1 Aµ

19 Lowest string states open string: α µ 0 > 1 Aµ d D x g tr (F µν F µν )

20 Lowest string states open string: α µ 0 > 1 Aµ d D x g tr (F µν F µν ) open strings lead to gauge fields (and matter)

21 Lowest string states open string: α µ 0 > 1 Aµ d D x g tr (F µν F µν ) open strings lead to gauge fields (and matter) closed string: level matching n N n = n N n

22 Lowest string states open string: α µ 0 > 1 Aµ d D x g tr (F µν F µν ) open strings lead to gauge fields (and matter) closed string: level matching n N n = n N n α µ 1ᾱν 1 0 > g µν,...

23 Lowest string states open string: α µ 0 > 1 Aµ d D x g tr (F µν F µν ) open strings lead to gauge fields (and matter) closed string: level matching n α µ 1ᾱν 1 0 > g µν,... N n = N n n d D x gr +

24 Lowest string states open string: α µ 0 > 1 Aµ d D x g tr (F µν F µν ) open strings lead to gauge fields (and matter) closed string: level matching n α µ 1ᾱν 1 0 > g µν,... N n = N n n d D x gr + closed strings leads to gravity (and gravity-like physics)

25 On closer examination:

26 On closer examination: There are five types of string theory (IIA, IIB, I, two heterotic).

27 On closer examination: There are five types of string theory (IIA, IIB, I, two heterotic). All five string theories are only consistent in 10 space-time dimensions.

28 On closer examination: There are five types of string theory (IIA, IIB, I, two heterotic). All five string theories are only consistent in 10 space-time dimensions. All five string theories have world sheet supersymmetry and lead to space-time supersymmetry in ten dimensions.

29 On closer examination: There are five types of string theory (IIA, IIB, I, two heterotic). All five string theories are only consistent in 10 space-time dimensions. All five string theories have world sheet supersymmetry and lead to space-time supersymmetry in ten dimensions. And there are more surprises...

30 T-duality

31 T-duality Modes of a string on a circle with radius R : R

32 T-duality Modes of a string on a circle with radius R : R momentum states : winding states : full spectrum : M 2 = m2 R 2 M 2 = w2 R 2 l 4 S m Z w Z M 2 = m2 R 2 + w2 R 2 l 4 S

33 T-duality Modes of a string on a circle with radius R : R momentum states : winding states : full spectrum : M 2 = m2 R 2 M 2 = w2 R 2 l 4 S m Z w Z M 2 = m2 R 2 + w2 R 2 l 4 S R

34 T-duality Modes of a string on a circle with radius R : R momentum states : winding states : full spectrum : M 2 = m2 R 2 M 2 = w2 R 2 l 4 S m Z w Z M 2 = m2 R 2 + w2 R 2 l 4 S R R

35 T-duality Modes of a string on a circle with radius R : R momentum states : winding states : full spectrum : M 2 = m2 R 2 M 2 = w2 R 2 l 4 S m Z w Z M 2 = m2 R 2 + w2 R 2 l 4 S R R R

36 T-duality Modes of a string on a circle with radius R : R momentum states : winding states : full spectrum : M 2 = m2 R 2 M 2 = w2 R 2 l 4 S m Z w Z M 2 = m2 R 2 + w2 R 2 l 4 S R R R T-duality: spectrum invariant under m w R l2 S R

37 T-duality Modes of a string on a circle with radius R : R momentum states : winding states : full spectrum : M 2 = m2 R 2 M 2 = w2 R 2 l 4 S m Z w Z M 2 = m2 R 2 + w2 R 2 l 4 S R R R T-duality: spectrum invariant under m w R l2 S R String theory has minimal length l s = α

38 Branes

39 Branes String theory contains not just strings but extended objects (p-branes) of all dimensions!

40 Branes String theory contains not just strings but extended objects (p-branes) of all dimensions!... N (D)p-brane(s) : U(N) gauge theory d=10/11 bulk gravity...

41 Branes String theory contains not just strings but extended objects (p-branes) of all dimensions!... N (D)p-brane(s) : U(N) gauge theory d=10/11 bulk gravity... p-branes are charged under (p+1) forms A µ1...µ p+1 field strength F = da. with

42 Branes String theory contains not just strings but extended objects (p-branes) of all dimensions!... N (D)p-brane(s) : U(N) gauge theory d=10/11 bulk gravity... p-branes are charged under (p+1) forms A µ1...µ p+1 field strength F = da. with bulk -> gravity (closed strings) brane -> gauge theories (open strings)

43 M-theory and branes

44 M-theory and branes All five string theories are related and part of a single theory : M-theory

45 M-theory and branes All five string theories are related and part of a single theory : M-theory d=11 1 SUGRA 1 S S /Z T T S IIB IIA heterotic I 2 heterotic II I

46 M-theory and branes All five string theories are related and part of a single theory : M-theory d=11 1 SUGRA 1 S S /Z IIB IIA heterotic I M T T S 2 heterotic II I

47 M-theory and branes All five string theories are related and part of a single theory : M-theory d=11 1 SUGRA 1 S S /Z IIB IIA heterotic I M T T S 2 heterotic II I M-theory is a patchwork of the constituent theories plus many rules. It seems unclear, at present, what its fundamental degrees of freedom are.

48 String theory and the real world (?)

49 String theory and the real world (?) Need to compactify six or seven dimensions to obtain d=4 theory :

50 String theory and the real world (?) Need to compactify six or seven dimensions to obtain d=4 theory : d=10/11 string/m-theory on d=6/7 dimensional space X d=4 theory

51 String theory and the real world (?) Need to compactify six or seven dimensions to obtain d=4 theory : d=10/11 string/m-theory on d=6/7 dimensional space X d=4 theory Two-fold degeneracy in space X: continuous one in size and shape (moduli), discrete one topology

52 String theory and the real world (?) Need to compactify six or seven dimensions to obtain d=4 theory : d=10/11 string/m-theory on d=6/7 dimensional space X d=4 theory Two-fold degeneracy in space X: continuous one in size and shape (moduli), discrete one topology But d=4 theory depends on space X...

53 The enemy

54 The enemy different moduli :

55 The enemy different moduli : different topology :

56 The enemy different moduli : different topology : topology: determines structure of d=4 theory

57 The enemy different moduli : different topology : topology: determines structure of d=4 theory moduli: determine values of coupling constants in d=4

58 The enemy different moduli : different topology : topology: determines structure of d=4 theory moduli: determine values of coupling constants in d=4 -> string theory does impose constraint on compactifications, however, there are still many choices -> many four-dimensional theories with moduli appearing as scalar fields.

59 The enemy different moduli : different topology : topology: determines structure of d=4 theory moduli: determine values of coupling constants in d=4 -> string theory does impose constraint on compactifications, however, there are still many choices -> many four-dimensional theories with moduli appearing as scalar fields. in simplest model and perturbatively : no D=4 potential for moduli

60 The world according to string/m-theory

61 The world according to string/m-theory d=6/7 internal space X

62 The world according to string/m-theory d=6/7 internal space X 3 external dimensions 6-brane

63 The world according to string/m-theory d=6/7 internal space X 3 external dimensions 6-brane 6-brane

64 The world according to string/m-theory d=6/7 internal space X 3 external dimensions 6-brane 6-brane 8-brane

65 The world according to string/m-theory d=6/7 internal space X 3 external dimensions 6-brane 6-brane 8-brane 3-brane

66 The world according to string/m-theory matter d=6/7 internal space X 3 external dimensions 6-brane 6-brane 8-brane 3-brane

67 The world according to string/m-theory matter d=6/7 internal space X matter 3 external dimensions 6-brane 6-brane 8-brane 3-brane

68 The world according to string/m-theory matter d=6/7 internal space X matter 3 external dimensions (S)SM 6-brane 6-brane 8-brane 3-brane

69 The world according to string/m-theory matter d=6/7 internal space X matter 3 external dimensions (S)SM??? 6-brane 6-brane 8-brane 3-brane

70 The world according to string/m-theory matter d=6/7 internal space X matter 3 external dimensions??? 6-brane 6-brane 8-brane 3-brane

71 The world according to string/m-theory matter d=6/7 internal space X matter 3 external dimensions 6-brane 6-brane 8-brane 3-brane

72 The world according to string/m-theory matter d=6/7 internal space X matter 3 external dimensions (S)SM 6-brane 6-brane 8-brane 3-brane

73 The world according to string/m-theory matter d=6/7 internal space X matter 3 external dimensions??? (S)SM 6-brane 6-brane 8-brane 3-brane

74 The world according to string/m-theory matter d=6/7 internal space X matter 3 external dimensions??? (S)SM 6-brane 6-brane 8-brane 3-brane And this is not just pictures...

75 Let us consider in D=10/11 :

76 Let us consider in D=10/11 : S D = 1 l D 2 S gravity... d D x g R +...

77 Let us consider in D=10/11 : S D = 1 l D 2 S gravity... d D x g R l p 3 S...and a p-brane d p+1 x γ tr ( F αβ F αβ) +...

78 Let us consider in D=10/11 : S D = 1 l D 2 S gravity... d D x g R l p 3 S...and a p-brane d p+1 x γ tr ( F αβ F αβ) +... compactification on : d=6,7 space X, volume V

79 Let us consider in D=10/11 : S D = 1 l D 2 S compactification on : gravity... d D x g R l p 3 S d=6,7 space X, volume V...and a p-brane d p+1 x γ tr ( F αβ F αβ) +... (p-3) cycle with volume v p-brane on (p-3) cycle

80 Let us consider in D=10/11 : S D = 1 l D 2 S compactification on : gravity... d D x g R l p 3 S d=6,7 space X, volume V...and a p-brane d p+1 x γ tr ( F αβ F αβ) +... (p-3) cycle with volume v p-brane on (p-3) cycle in D=4 : S 4 = d 4 x V l D 2 S g4 R

81 Let us consider in D=10/11 : S D = 1 l D 2 S compactification on : gravity... d D x g R l p 3 S d=6,7 space X, volume V...and a p-brane d p+1 x γ tr ( F αβ F αβ) +... (p-3) cycle with volume v p-brane on (p-3) cycle in D=4 : S 4 = d 4 x V l D 2 S g4 R d 4 x v l p 3 S g4 tr (F µν F µν ) +...

82 Let us consider in D=10/11 : S D = 1 l D 2 S compactification on : gravity... d D x g R l p 3 S d=6,7 space X, volume V...and a p-brane d p+1 x γ tr ( F αβ F αβ) +... (p-3) cycle with volume v p-brane on (p-3) cycle in D=4 : S 4 = d 4 x V l D 2 S g4 R d 4 x v l p 3 S g4 tr (F µν F µν ) πG N = V l D 2 S

83 Let us consider in D=10/11 : S D = 1 l D 2 S compactification on : gravity... d D x g R l p 3 S d=6,7 space X, volume V...and a p-brane d p+1 x γ tr ( F αβ F αβ) +... (p-3) cycle with volume v p-brane on (p-3) cycle in D=4 : S 4 = d 4 x V l D 2 S g4 R d 4 x v l p 3 S g4 tr (F µν F µν ) πG N = V l D 2 S 1 16πg 2 YM = v l p 3 S

84 it follows : For large volume, the string scale can be smaller than the Planck scale (but one has to find a stabilising potential for V).

85 it follows : For large volume, the string scale can be smaller than the Planck scale (but one has to find a stabilising potential for V). On a single stack of branes, the gauge coupling is universal and depends on the volume of the cycle wrapped.

86 One stack versus several stacks Two phenomenological facts:

87 One stack versus several stacks Two phenomenological facts: Gauge couplings unify in MSSM

88 One stack versus several stacks Two phenomenological facts: Gauge couplings unify in MSSM One SM family fits into 16 representation of SO(10)

89 One stack versus several stacks Two phenomenological facts: Gauge couplings unify in MSSM One SM family fits into 16 representation of SO(10) This hints at single stack models, since

90 One stack versus several stacks Two phenomenological facts: Gauge couplings unify in MSSM One SM family fits into 16 representation of SO(10) This hints at single stack models, since they lead to a universal gauge coupling

91 One stack versus several stacks Two phenomenological facts: Gauge couplings unify in MSSM One SM family fits into 16 representation of SO(10) This hints at single stack models, since they lead to a universal gauge coupling matter fields descend from higher-dim. gauge theory with large gauge group

92 One stack versus several stacks Two phenomenological facts: Gauge couplings unify in MSSM One SM family fits into 16 representation of SO(10) This hints at single stack models, since they lead to a universal gauge coupling matter fields descend from higher-dim. gauge theory with large gauge group for example : 248 E8 [(45, 1) + (1, 15) + (16, 4) + ( 16, 4) + (10, 6)] SO(10) SU(4)

93 One stack versus several stacks Two phenomenological facts: Gauge couplings unify in MSSM One SM family fits into 16 representation of SO(10) This hints at single stack models, since they lead to a universal gauge coupling matter fields descend from higher-dim. gauge theory with large gauge group for example : 248 E8 [(45, 1) + (1, 15) + (16, 4) + ( 16, 4) + (10, 6)] SO(10) SU(4) one standard model family

94 Moduli stabilisation and flux What is flux?

95 Moduli stabilisation and flux What is flux? A: Non-zero form field strengths, F 0, on the internal space.

96 Moduli stabilisation and flux What is flux? A: Non-zero form field strengths, F 0, on the internal space. Moduli types: T (size of X), Z (shape of X),...

97 Moduli stabilisation and flux What is flux? A: Non-zero form field strengths, F 0, on the internal space. Moduli types: T (size of X), Z (shape of X),... Without flux, perturbatively: W moduli = 0 V moduli = 0

98 Moduli stabilisation and flux What is flux? A: Non-zero form field strengths, F 0, on the internal space. Moduli types: T (size of X), Z (shape of X),... Without flux, perturbatively: W moduli = 0 V moduli = 0 Non-perturbative effects: W moduli e T V b

99 Moduli stabilisation and flux What is flux? A: Non-zero form field strengths, F 0, on the internal space. Moduli types: T (size of X), Z (shape of X),... Without flux, perturbatively: W moduli = 0 V moduli = 0 Non-perturbative effects: W moduli e T V b Flux: For example W moduli = P (Z), non-exponential, fixes Z.

100 Moduli stabilisation and flux What is flux? A: Non-zero form field strengths, F 0, on the internal space. Moduli types: T (size of X), Z (shape of X),... Without flux, perturbatively: W moduli = 0 V moduli = 0 Non-perturbative effects: W moduli e T V b Flux: For example W moduli = P (Z), non-exponential, fixes Z. Flux and non-pert.: W moduli = P (Z) + e T V!!"!#" b

101 Moduli stabilisation and flux What is flux? A: Non-zero form field strengths, F 0, on the internal space. Moduli types: T (size of X), Z (shape of X),... Without flux, perturbatively: W moduli = 0 V moduli = 0 Non-perturbative effects: W moduli e T V b Flux: For example W moduli = P (Z), non-exponential, fixes Z. Flux and non-pert.: W moduli = P (Z) + e T V Fixes all moduli, cosmological constant needs tuning.!#"!!" b

102 There appears to be a huge number of such stable models (10 500?) and it seems string theory does not discriminate between them. Is this a problem?

103 There appears to be a huge number of such stable models (10 500?) and it seems string theory does not discriminate between them. Is this a problem? It may be a problem in principle, but how can we be sure before the fundamental formulation of the theory is known?

104 There appears to be a huge number of such stable models (10 500?) and it seems string theory does not discriminate between them. Is this a problem? It may be a problem in principle, but how can we be sure before the fundamental formulation of the theory is known? It is certainly a problem in practice, so what can string phenomenology do?

105 There appears to be a huge number of such stable models (10 500?) and it seems string theory does not discriminate between them. Is this a problem? It may be a problem in principle, but how can we be sure before the fundamental formulation of the theory is known? It is certainly a problem in practice, so what can string phenomenology do? One can construct (supersymmetric) standard-like models with the right generic properties (gauge group has SU(3)xSU(2)xU(1) factor, 3 generations, Higgs multiplets).

106 There appears to be a huge number of such stable models (10 500?) and it seems string theory does not discriminate between them. Is this a problem? It may be a problem in principle, but how can we be sure before the fundamental formulation of the theory is known? It is certainly a problem in practice, so what can string phenomenology do? One can construct (supersymmetric) standard-like models with the right generic properties (gauge group has SU(3)xSU(2)xU(1) factor, 3 generations, Higgs multiplets). A fully viable SSM from string theory has yet to be constructed (no additional light particles, right Yukawa couplings,...). Additional physics constraints tend to reduce number of viable models dramatically. In this sense, we have too few models!

107 There appears to be a huge number of such stable models (10 500?) and it seems string theory does not discriminate between them. Is this a problem? It may be a problem in principle, but how can we be sure before the fundamental formulation of the theory is known? It is certainly a problem in practice, so what can string phenomenology do? One can construct (supersymmetric) standard-like models with the right generic properties (gauge group has SU(3)xSU(2)xU(1) factor, 3 generations, Higgs multiplets). A fully viable SSM from string theory has yet to be constructed (no additional light particles, right Yukawa couplings,...). Additional physics constraints tend to reduce number of viable models dramatically. In this sense, we have too few models! What needs to be done to find a SSM from string theory? - Need to construct large numbers of models. - Need to combine this with moduli stabilisation.

108 Recent Work (Lara Anderson, Yang-Hui He, A.L.)

109 Recent Work Model building for E 8 E 8 (Lara Anderson, Yang-Hui He, A.L.) heterotic string/m-theory

110 Recent Work Model building for E 8 E 8 (Lara Anderson, Yang-Hui He, A.L.) heterotic string/m-theory MSSM? hidden sector hidden sector 9-brane 5-brane 9-brane

111 Recent Work Model building for E 8 E 8 (Lara Anderson, Yang-Hui He, A.L.) heterotic string/m-theory Calabi-Yau manifold X MSSM? hidden sector hidden sector 9-brane 5-brane 9-brane

112 Recent Work Model building for E 8 E 8 (Lara Anderson, Yang-Hui He, A.L.) heterotic string/m-theory Calabi-Yau manifold X holomorphic vector bundle V 1 MSSM? hidden sector hidden sector 9-brane 5-brane 9-brane

113 Recent Work Model building for E 8 E 8 (Lara Anderson, Yang-Hui He, A.L.) heterotic string/m-theory Calabi-Yau manifold X holomorphic vector bundle V 1 holomorphic vector bundle V 2 MSSM? hidden sector hidden sector 9-brane 5-brane 9-brane

114 Recent Work (Lara Anderson, Yang-Hui He, A.L.) Model building for E 8 E 8 heterotic string/m-theory holomorphic curve W Calabi-Yau manifold X holomorphic vector bundle V 1 holomorphic vector bundle V 2 MSSM? hidden sector hidden sector 9-brane 5-brane 9-brane

115 Recent Work (Lara Anderson, Yang-Hui He, A.L.) Model building for E 8 E 8 heterotic string/m-theory holomorphic curve W Calabi-Yau manifold X holomorphic vector bundle V 1 holomorphic vector bundle V 2 MSSM? hidden sector hidden sector m 3 2 M 2 S M P l SUSY at M S 9-brane 5-brane 9-brane

116 Recent Work (Lara Anderson, Yang-Hui He, A.L.) Model building for E 8 E 8 heterotic string/m-theory holomorphic curve W Calabi-Yau manifold X holomorphic vector bundle V 1 holomorphic vector bundle V 2 MSSM? hidden sector hidden sector m 3 2 M 2 S M P l SUSY at M S 9-brane 5-brane 9-brane Data describing model: CY, bundles and curve. X V 1 V 2 W

117 Consistency condition: c 2 (T X) c 2 (V 1 ) c 2 (V 2 ) = [W ]

118 Consistency condition: c 2 (T X) c 2 (V 1 ) c 2 (V 2 ) = [W ] For SUSY: [W ] 0 and V 1, V 2 stable bundles (hard to prove).

119 Consistency condition: c 2 (T X) c 2 (V 1 ) c 2 (V 2 ) = [W ] For SUSY: [W ] 0 and V 1, V 2 stable bundles (hard to prove). How do we construct bundles V on X?

120 Consistency condition: c 2 (T X) c 2 (V 1 ) c 2 (V 2 ) = [W ] For SUSY: [W ] 0 and V 1, V 2 stable bundles (hard to prove). How do we construct bundles V on X? monads 0 V r B i=1 O X (b i ) r C j=1 O X (c j ) 0

121 Consistency condition: c 2 (T X) c 2 (V 1 ) c 2 (V 2 ) = [W ] For SUSY: [W ] 0 and V 1, V 2 stable bundles (hard to prove). How do we construct bundles V on X? monads 0 V r B i=1 O X (b i ) For a start we produced a list of 5000 CY manifolds and computed their properties, such as c 2 (T X). r C j=1 O X (c j ) 0

122 Consistency condition: c 2 (T X) c 2 (V 1 ) c 2 (V 2 ) = [W ] For SUSY: [W ] 0 and V 1, V 2 stable bundles (hard to prove). How do we construct bundles V on X? monads 0 V r B i=1 O X (b i ) For a start we produced a list of 5000 CY manifolds and computed their properties, such as c 2 (T X). Goal: Construct all stable (SU(3),SU(4),SU(5)) monad bundles V on these CYs, such that c 2 (T X) c 2 (V ) 0 and the number of generations is a multiple of three. r C j=1 Compute the complete spectrum. O X (c j ) 0

123 Consistency condition: c 2 (T X) c 2 (V 1 ) c 2 (V 2 ) = [W ] For SUSY: [W ] 0 and V 1, V 2 stable bundles (hard to prove). How do we construct bundles V on X? monads 0 V r B i=1 O X (b i ) For a start we produced a list of 5000 CY manifolds and computed their properties, such as c 2 (T X). Goal: Construct all stable (SU(3),SU(4),SU(5)) monad bundles V on these CYs, such that c 2 (T X) c 2 (V ) 0 and the number of generations is a multiple of three. r C j=1 Compute the complete spectrum. leading to E6, SO(10),SU(5) GUTs O X (c j ) 0

124 We decided to start with the 5 simplest of the 5000 CYs.

125 We decided to start with the 5 simplest of the 5000 CYs. Results: 37 models, no anti-generations...

126 We decided to start with the 5 simplest of the 5000 CYs. Results: 37 models, no anti-generations E 6 models

127 We decided to start with the 5 simplest of the 5000 CYs. Results: 37 models, no anti-generations E 6 models 10 SO(10) models

128 We decided to start with the 5 simplest of the 5000 CYs. Results: 37 models, no anti-generations E 6 models 10 SO(10) models 7 SU(5) models

129 We decided to start with the 5 simplest of the 5000 CYs. Results: 37 models, no anti-generations E 6 models 10 SO(10) models 7 SU(5) models We are currently extending this to all 5000 CYs

130 Conclusion String theory realises gravity and gauge theories through closed and open strings (bulk and brane) and has all the right generic ingredients to make contact with particle physics.

131 Conclusion String theory realises gravity and gauge theories through closed and open strings (bulk and brane) and has all the right generic ingredients to make contact with particle physics. Most ideas for BSM physics are either motivated by string theory or contained in string theory.

132 Conclusion String theory realises gravity and gauge theories through closed and open strings (bulk and brane) and has all the right generic ingredients to make contact with particle physics. Most ideas for BSM physics are either motivated by string theory or contained in string theory. Matter fields can arise from either brane intersections or gauge fields on high-dimensional branes. The latter possibility seems preferable.

133 Conclusion String theory realises gravity and gauge theories through closed and open strings (bulk and brane) and has all the right generic ingredients to make contact with particle physics. Most ideas for BSM physics are either motivated by string theory or contained in string theory. Matter fields can arise from either brane intersections or gauge fields on high-dimensional branes. The latter possibility seems preferable. There appears to be a huge number of consistent string vacua. Given the fundamental formulation of the theory is not known one should be careful about jumping to conclusions.

134 Conclusion String theory realises gravity and gauge theories through closed and open strings (bulk and brane) and has all the right generic ingredients to make contact with particle physics. Most ideas for BSM physics are either motivated by string theory or contained in string theory. Matter fields can arise from either brane intersections or gauge fields on high-dimensional branes. The latter possibility seems preferable. There appears to be a huge number of consistent string vacua. Given the fundamental formulation of the theory is not known one should be careful about jumping to conclusions. One can construct standard-like models, but there is not a single standard model from string theory.

135 Conclusion String theory realises gravity and gauge theories through closed and open strings (bulk and brane) and has all the right generic ingredients to make contact with particle physics. Most ideas for BSM physics are either motivated by string theory or contained in string theory. Matter fields can arise from either brane intersections or gauge fields on high-dimensional branes. The latter possibility seems preferable. There appears to be a huge number of consistent string vacua. Given the fundamental formulation of the theory is not known one should be careful about jumping to conclusions. One can construct standard-like models, but there is not a single standard model from string theory. The ability to stabilise all moduli has opened up new possibilities for string phenomenology. E.g. the computation of Yukawa couplings for given models seems now feasible, although it is technically hard.

136 Deriving a SSM with the right particle content and couplings from string theory would be a major success.

137 Deriving a SSM with the right particle content and couplings from string theory would be a major success. Should the LHC discover physics which points towards string theory (SUSY, KK modes,...) string phenomenology will get a substantial boost.

138 Deriving a SSM with the right particle content and couplings from string theory would be a major success. Should the LHC discover physics which points towards string theory (SUSY, KK modes,...) string phenomenology will get a substantial boost. Thanks!