F- 理論におけるフラックスコンパクト化. Hajime Otsuka( 大塚啓 ) (Waseda U.) Physics Lett. B. 774 (2017) 225 with Y. Honma (National Tsing-Hua U.) Sangyo U.
|
|
- Gabriel Phillips
- 5 years ago
- Views:
Transcription
1 F- 理論におけるフラックスコンパクト化 Hajime Otsuka( 大塚啓 ) (Waseda U.) Physics Lett. B. 774 (2017) 225 with Y. Honma (National Tsing-Hua U.) 2018/1/29@Kyoto Sangyo U.
2 Outline Introduction Flux compactification in type IIB string Flux compactification in F-theory i) F-theory ii) Setup iii) Flux compactification Conclusion
3 Introduction The standard model of particle physics Gauge group:su(3) SU(2) U(1) Matter content: 3
4 Introduction Problem: No gravitational interaction in the standard model String theory A good candidate for the unified theory of the gauge and gravitational interactions Closed string Graviton Dp-brane Ramond-Ramond field: C p+1 4
5 Introduction Problem: No gravitational interaction in the standard model String theory A good candidate for the unified theory of the gauge and gravitational interactions Closed string Graviton Open string Dp-brane Ramond-Ramond field: C p+1 Gauge fields 5
6 (Perturbative) superstring theory requires the extra 6 dimension. 10=4+6 The geometric parameters of extra 6D dimensions 4D scalar fields (called moduli) Unless they are stabilized, it will lead to unobserved fifth forces. Stabilization of the extra dimensional space Moduli stabilization (creating a moduli potential) 6D Calabi-Yau (CY)Manifold R ij = 0
7 Moduli are ubiquitous in string compactifications Good candidate of inflaton Supersymmetry breaking Moduli cosmology Moduli interact with matter fields gravitationally. Such long-lived particles affects the cosmology of the early Universe (e.g., dark matter abundance, baryon asymmetry, )
8 Yukawa couplings In string theory as well as the higher-dimensional theory, Yukawa couplings Overlap integral of matter wave functions λ Yukawa = න ψφψ CY Yukawa couplings depend on the moduli fields. From such phenomenological points of view, it is quite important to discuss the moduli dynamics.
9 Two types of moduli fields (4D massless scalar fields): 1Closed string moduli i) Dilaton ( τ ) Imτ = g s 1 g s : string coupling ii) Kähler moduli ( δg ij ) Size of the internal cycles iii) Complex structure moduli (δg i j ) Shape
10 Two types of moduli fields (4D massless scalar fields): Dp-brane Gauge fields: A μ (μ = 0,1, p) x a Scalar field : Φ a (a = p + 1,, 9)
11 Two types of moduli fields (4D massless scalar fields): Dp-brane 2Open string moduli A i (i = 4,5,.., p) Φ a (a = p + 1,, 9) Gauge fields: A μ (μ = 0,1, p) x a Scalar field : Φ a (a = p + 1,, 9)
12 Two types of moduli fields (4D massless scalar fields): 1Closed string moduli 2Open string moduli Moduli dynamics will give significant effects to our Universe. In this talk, we consider the stabilization of both the open and closed string moduli based on F-theory ( non-perturbative description of IIB string).
13 Outline Introduction Flux compactification in type IIB string Flux compactification in F-theory i) F-theory ii) Setup iii) Flux compactification Conclusion
14 Flux compactification Flux compactification is useful to stabilize the moduli fields. Let us consider higher-dimensional Maxwell s theory on R 1,3 M, න F p F p R 1,3 M When then exists a magnetic flux F p in a cycle Σ p of M න Σ p F p = n Z It generates a potential depending on the metric of extra dimension. 14
15 Flux compactification in type IIB string on CY Type IIB string on R 1,3 CY, න G 3 G 3 R 1,3 CY G 3 = F 3 τh 3 : three-form The fluxes on the three-cycle of CY (Σ 3 ) generate the moduli potential, න Σ 3 F 3 In the 4D low-energy effective action, Flux-induced superpotential: න H 3 Σ 3 [Gukov-Vafa-Witten 99] W τ, z = න G 3 Ω z CY Ω(z) : hol. (3,0) form of CY z: Complex structure moduli 15
16 Low-energy effective action described by 4D N=1 SUGRA K = ln i Ω ഥΩ ln i τ τ 2 ln(v(t)) W τ, z = CY G 3 τ Ω z Ω(z) : hol. (3,0) form of CY V(T) : CY Volume V = e K ቌ K IJ D I WD I,J=τ,z JW + (K T തT K T K തT 3) W 2 = 0 No-scale structure ቍ D I = I + K I K I = I K in the reduced Planck unit M pl = 1 Dilaton and complex structure moduli are stabilized at D τ W = D z W = 0 16
17 Low-energy effective action described by 4D N=1 SUGRA K = ln i Ω ഥΩ ln i τ τ 2 ln(v(t)) W τ, z = CY G 3 τ Ω z Ω(z) : hol. (3,0) form of CY V(T) : CY Volume V = e K ቌ K IJ D I WD I,J=τ,z JW + (K T തT K T K തT 3) W 2 = 0 No-scale structure ቍ D I = I + K I K I = I K in the reduced Planck unit M pl = 1 Dilaton and complex structure moduli are stabilized at D τ W = D z W = 0 17
18 Dilaton and complex structure moduli are stabilized at D τ W = D z W = 0 W τ, z = න G 3 τ Ω z CY G 3 -fluxes are constrained as the imaginary self-dual fluxes: G 3 = i 6 G 3 Tadpole condition for C 4 : G 3 = F 3 τh 3 : three-form න H 3 F 3 + Q D3 = 0 CY 18
19 Dilaton and complex structure moduli are stabilized at D τ W = D z W = 0 W τ, z = න G 3 τ Ω z CY G 3 -fluxes are constrained as the imaginary self-dual fluxes: G 3 = i 6 G 3 Tadpole condition for C 4 : න C 4 G 3 G 3 10D G 3 = F 3 τh 3 න C4 : three-form න H 3 F 3 + Q D3 = 0 CY 19
20 How do we compute the flux-induced superpotential? W = න G 3 Ω CY G 3 = F 3 τh 3 : three-form Let us expand G 3 and Ω on the integral symplectic basis (α a, β a ) of H 3 (CY, Z), F 3 H 3 G 3 = M a α a N a β a τ( M a α a N a β a ) α a β b = δ a b a, b = 0,1,, h 2,1 Period vector : Ω = X a α a F a β a Π t = F a = F X a න A a Ω, න B a Ω = (X a, F a ) Quantized fluxes (A a, B a : basis of 3-cycles in CY)
21 How do we compute the flux-induced superpotential? W = න G 3 Ω = n F τn H Π CY G 3 = F 3 τh 3 : three-form Let us expand G 3 and Ω on the integral symplectic basis (α a, β a ) of H 3 (CY, Z), F 3 H 3 G 3 = M a α a N a β a τ( M a α a N a β a ) α a β b = δ a b a, b = 0,1,, h 2,1 Period vector : Ω = X a α a F a β a Π t = F a = F X a න A a Ω, න B a Ω = (X a, F a ) Quantized fluxes (A a, B a : basis of 3-cycles in CY)
22 Period integral Π t = න Ω, න Ω = (X a, F a ) A a B a can be exactly calculated by solving the Picard-Fuchs (PF) equation. For mirror quintic CY PF equation: z 5ψ 5 P ψ (h 2,1 = 1) 5 = x 5 i ψx 1 x 2 x 3 x 4 x 5 = 0 in an orbifold of CP 4 i=1 Complex structure moduli x 1, x 2, x 3, x 4, x 5 λx 1, λx 2, λx 3, λx 4, λx 5 ൭z d dz ൱ 4 5z ൭5z d ൱ dz + 1 ൭5z d dz + 2൱ ൭5z d dz + 3൱ ൭5z d dz + 4൱ Π = 0 Δ Ω = න P=0 P(ψ) Δ: 4-form in CP 4 [Candelas et al, 91]
23 Period integral Π t = න Ω, න Ω = (X a, F a ) A a B a can be exactly calculated by solving the Picard-Fuchs (PF) equation. For mirror quintic CY PF equation: z 5ψ 5 P ψ (h 2,1 = 1) 5 = x 5 i ψx 1 x 2 x 3 x 4 x 5 = 0 in an orbifold of CP 4 i=1 Complex structure moduli x 1, x 2, x 3, x 4, x 5 λx 1, λx 2, λx 3, λx 4, λx 5 ൭z d dz ൱ 4 5z ൭5z d ൱ dz + 1 ൭5z d dz + 2൱ ൭5z d dz + 3൱ ൭5z d dz + 4൱ Π = 0 E.g., in the large complex structure limit ψ 1 (z 1), Π Π 2 5 ln 2 z 2 2πi 2 + ln z Π 3 5 ln 3 z Π 6 2πi πi + [Candelas et al, 91]
24 4D effective potential: Previous mirror quintic CY can be engineered by 2D N=(2,2) U(1) Gauged Linear Sigma Model with 6 chiral superfields Φ 0,1,,5 Picard-Fuchs operator: W = න G 3 Ω = n F τn H Π CY K = ln Π i Σ ij Π j ln i τ τ U(1) charges (Toric charges) l = (l 0, l 1, l 2, l 3, l 4, l 5 ) = 1 D = a 0 Π li >0 ൭ l i ൱ Π a li<0 i ൭ ൱ a i 2 ln(v(t)) Σ ij : Symplectic matrix Stabilization of complex structure moduli and dilaton 5,1,1,1,1,1 l i z 1 l0πi=0 n [Witten 93] a i l i [Hosono-Klemm-Theisen-Yau, 93]
25 Comment on the Kähler Moduli stabilization The remaining Kähler moduli (T) can be stabilized by the nonperturbative effects. W =< W flux > +Ae at A, a : Constants KKLT scenario (< W flux > 1 ) LARGE volume scenario (< W flux > O(1) ) [Kachru-Kallosh-Linde-Trivedi 03] [Balasubramanian-Berglund-Conlon-Quevedo 05] De Sitter vacua can be realized by introducing the anti D3-branes. Radiative moduli stabilization scenario [Kobayashi-Omoto-Otsuka-Tatsuishi 18] 25
26 Outline Introduction Flux compactification in type IIB string Flux compactification in F-theory i) F-theory ii) Setup iii) Flux compactification Conclusion
27 Type IIB action in Einstein frame(with other fields set to 0): L IIB = g ൭R τ 2 ൱ 2(Im τ) 2 where τ = C 0 + ie φ, This action is invariant under SL 2, Z : ( Imτ = g s 1, g s : string coupling) τ τ + 1, τ 1/τ
28 Type IIB action in Einstein frame(with other fields set to 0): L IIB = g ൭R τ 2 ൱ 2(Im τ) 2 where τ = C 0 + ie φ, This action is invariant under SL 2, Z : ( Imτ = g s 1, g s : string coupling) τ τ + 1, τ 1/τ Interpret τ as complex structure of auxiliary torus T 2 (Vafa 96) T 2 = τ τ
29 F-theory is defined in 12 D spacetime 12=4+8 u 0 u τ(u) 6D manifold τ u : dilaton g s = Im τ 1 g s : string coupling 8D CY manifold String coupling can be taken as g s = Im τ 1 > 1. F-theory = non-perturbative description of type IIB
30 D7-brane looks like cosmic string in ambient space (Greene, Shapere, Vafa, Yau, 89) Metric: 7 ds 2 10 = dt 2 + dx 2 i + H u, തu dud തu i=1 D7 D7-brane has magnetic charge under C 0 1 = ර u=u 0 dc 0 = C 0 ue 2πi C 0 u u 0 τ D7-brane
31 D7-brane looks like cosmic string in ambient space (Greene, Shapere, Vafa, Yau, 89) Metric: 7 ds 2 10 = dt 2 + dx 2 i + H u, തu dud തu i=1 D7 D7-brane has magnetic charge under C 0 1 = ර dc 0 = C 0 u=u 0 ue 2πi C 0 u C 0 = Reτ Near D7-brane : τ 1 2πi 0 D7-brane location : τ u 0 i (T 2 degenerate at u = u 0.) u 0 τ D7-brane
32 D7-brane looks like cosmic string in ambient space (Greene, Shapere, Vafa, Yau, 89) Metric: 7 ds 2 10 = dt 2 + dx 2 i + H u, തu dud തu i=1 D7 D7-brane has magnetic charge under C 0 1 = ර dc 0 = C 0 u=u 0 ue 2πi C 0 u C 0 = Reτ Near D7-brane : τ 1 2πi 0 D7-brane location : τ u 0 i (T 2 degenerate at u = u 0.) u 0 u u 0 τ D7-brane τ(u) 6D manifold 8D CY manifold
33 F-theory is defined in 12 D spacetime 12=4+8 u τ(u) 3D Kähler manifold τ u : dilaton g s = Im τ 1 g s : string coupling 17-branes exist at the singular limit of torus Elliptically fibered CY fourfold (CY4) 2String coupling > 1 ( Non-perturbative description of type IIB superstring) 3 Both open and closed string moduli are involved.
34 Outline Introduction Flux compactification in type IIB string Flux compactification in F-theory i) F-theory ii) Setup iii) Flux compactification Conclusion
35 Brane Superpotential: W brane = න Ω Γ, Γ=C For branes wrapping on the whole CY, open string partition function is given by holomorphic Chern-Simons theory [Witten 92]: W = න Ω Tr[A CY A + 2 A A A] 3 Lower dimensional branes wrapping on holomorphic submanifold C can be obtained by dimensional reduction A φ [Aganagic-Vafa 00] W brane (ψ, φ) = Γ, Γ=C Ω Γ CY C
36 Brane superpotential (Open mirror symmetry) Mirror Quintic CY3 (degree 5 hypersurface in CP 4 ) Γ P ψ = σ5 i=1 x i 5 5ψx 1 x 2 x 3 x 4 x 5 = 0 Let us consider holomorphic 2-cycles where the brane wraps[morrison-walcher 07] C ± : x 1 + x 2 = 0, x 3 + x 4 = 0, x 5 2 ± 5ψx 1 x 3 = 0 W = න Ω No moduli dependence at fixed C ±! Brane deformation: Γ into (generically non-holomorphic) curve surrounded by a holomorphic divisor Γ C + C Mirror Quintic CY3
37 Brane superpotential (Open mirror symmetry) Mirror Quintic CY3 (degree 5 hypersurface in CP 4 ) Γ P ψ = σ5 i=1 x i 5 5ψx 1 x 2 x 3 x 4 x 5 = 0 Continuous deformation of C ± : (Hol. divisor defined by a degree 4 polynomial) Q φ = x 5 4 5φx 1 x 2 x 3 x 4 = 0 C C + φ = 5ψ φ = + 5ψ Mirror Quintic CY3 Brane superpotential: W brane ψ, φ Brane deformation = නΩ(ψ, φ) = න which is related to D7-brane with magnetic flux F Γ Γ, Γ=Q φ F Ω [Grimm-Ha-Klemm-Klevers 09]
38 Toric charges of the previous system, l = 5,1,1,1,1,1; 0,0 l = 1,0,0,0,0,1; 1, 1 l: Quintic CY3 l : brane deformation The period integral Π i = න Ω ψ, φ Γ i can be computed by solving the corresponding Picard-Fuchs equation. Brane and geometry cannot be distinguished. The above system is a noncompact CY4. (CY3 fibered over ) [Jockers-Soroush 08] Compactification CP 1 leads to a compact CY4.
39 CY3+brane CY4 without brane In the toric language, the previous system corresponds to A-model : Quintic CY3 over CP 1 [Berglund-Mayr 98, Grimm-Ha-Klemm-Klevers 09, Jockers-Mayr-Walcher 09] l 1 = 4,0,1,1,1,1, 1, 1,0 l 2 = 1,1,0,0,0,0,1, 1,0 l 3 = 0, 2,0,0,0,0,0,1,1 l 1 + l 2 : Quintic CY3 l 2 : brane deformation l 3 : base CP 1 B-model : Elliptically fibered CY4 [Berglund-Mayr 98]
40 F-theory compactification on elliptically fibered CY4 l 1 = 4,0,1,1,1,1, 1, 1,0 l 2 = 1,1,0,0,0,0,1, 1,0 l 3 = 0, 2,0,0,0,0,0,1,1 l 1 + l 2 : Quintic CY3 l 2 : brane deformation l 3 : base CP 1 Period vector of CY4 in the large complex structure limit z: Quintic modulus S: Dilaton z 1 : Open string modulus Π i = γ i Ω : Fourfold periods γ i : Homology basis of H 4 H CY4, Z
41 F-theory compactification on CY4 u 0 u τ(u) τ u : dilaton 3D Kähler manifold CY3+branes Complex structure moduli of CY3 Dilaton Open string (position) moduli Elliptically fibered CY4 Complex structure moduli of CY4
42 Outline Introduction Flux compactification in type IIB string Flux compactification in F-theory i) F-theory ii) Setup iii) Flux compactification Conclusion
43 F-theory on elliptically fibered CY4 4D N=1 supergravity In 4D N=1 SUGRA Kähler potential: Superpotential: K = ln න Ω ഥΩ 2ln V CY4 = ln(π i η ij ഥΠ j ) 2ln V W = න G 4 Ω = n i η ij Π j CY4 c [Gukov-Vafa-Witten, 99] Scalar potential: V = e K ቌ I,J c K I J D I WDJW ቍ Π i = γ i Ω : Fourfold periods n i = γ i G 4 : Quantized four-form fluxes γ i : Homology basis of H 4 H CY4, Z η ij : Topological intersection matrix V : Volume of 3D Kähler base
44 Flux compactification in F-theory on CY4 G 3 -flux superpotential + brane superpotential in type IIB =G 4 -flux superpotential in F-theory W = න G 4 Ω CY4 [Grimm-Ha-Klemm-Klevers 09, ] Imaginary self-dual three-form fluxes in type IIB =correspond to self-dual G 4 -fluxes G 4 = G 4 [Gukov-Vafa-Witten 99] Tadpole conditions χ 24 = n D න G 4 G 4 CY4 [Becker-Becker 96] [Sethi-Vafa-Witten 96] χ: Euler number of CY4 n D3 : # of D3
45 F-theory compactification on elliptically fibered CY4 z: Quintic modulus S: Dilaton z 1 : Open string modulus n i : Quantized fluxes Kähler potential: NLO in g s correction Superpotential:
46 F-theory compactification on elliptically fibered CY4 z: Quintic modulus S: Dilaton z 1 : Open string modulus n i : Quantized fluxes Kähler potential: NLO in g s correction Superpotential: The self-dual G 4 fluxes
47 Vacuum structure of F-theory As a consequence of the self-dual condition to G 4 fluxes, all the moduli fields are stabilized at VEVs: D S W = D z W = D z1 W = 0 z: Quintic modulus S: Dilaton z 1 : Open string modulus n i : Quantized fluxes
48 Vacuum structure of F-theory Although the fluxes are constrained by the tadpole condition, χ 24 = n D න G 4 G 4 CY4 χ=1860: Euler number of CY4 n D3 : # of D3 we find the consistent F-theory vacuum, e.g., All the moduli fields can be stabilized around the LCS point of CY fourfold The masses of all the moduli fields are positive definite.
49 Comment on other models in F-theory on CY4 The orientifold limit of F-theory [Dasgupta-Rajesh-Sethi 99, Denef-Douglas-Florea-Grassi-Kachru 05] K3 K3 background [Berglund-Mayr 13] Elliptically fibered CY4 in the large complex structure limit [Honma-Otsuka 17]
50 Conclusion Mirror symmetry techniques can be applied to the F-theory compactifications. We explicitly demonstrate the moduli stabilization around the large complex structure point of the F-theory fourfold. All the complex structure moduli can be stabilized at the Minkowski minimum. Discussion Quantum corrections to the moduli potential Other CY4 Particle spectra in global F-theory models Heterotic/F-theory duality
Stringy Corrections, SUSY Breaking and the Stabilization of (all) Kähler moduli
Stringy Corrections, SUSY Breaking and the Stabilization of (all) Kähler moduli Per Berglund University of New Hampshire Based on arxiv: 1012:xxxx with Balasubramanian and hep-th/040854 Balasubramanian,
More informationFixing all moduli in F-theory and type II strings
Fixing all moduli in F-theory and type II strings 0504058 Per Berglund, P.M. [0501139 D. Lüst, P.M., S. Reffert, S. Stieberger] 1 - Flux compactifications are important in many constructions of string
More informationF-theory effective physics via M-theory. Thomas W. Grimm!! Max Planck Institute for Physics (Werner-Heisenberg-Institut)! Munich
F-theory effective physics via M-theory Thomas W. Grimm Max Planck Institute for Physics (Werner-Heisenberg-Institut) Munich Ahrenshoop conference, July 2014 1 Introduction In recent years there has been
More informationString-Theory: Open-closed String Moduli Spaces
String-Theory: Open-closed String Moduli Spaces Heidelberg, 13.10.2014 History of the Universe particular: Epoch of cosmic inflation in the early Universe Inflation and Inflaton φ, potential V (φ) Possible
More informationInstantons in string theory via F-theory
Instantons in string theory via F-theory Andrés Collinucci ASC, LMU, Munich Padova, May 12, 2010 arxiv:1002.1894 in collaboration with R. Blumenhagen and B. Jurke Outline 1. Intro: From string theory to
More informationOn Flux Quantization in F-Theory
On Flux Quantization in F-Theory Raffaele Savelli MPI - Munich Bad Honnef, March 2011 Based on work with A. Collinucci, arxiv: 1011.6388 Motivations Motivations The recent attempts to find UV-completions
More informationGeneralized N = 1 orientifold compactifications
Generalized N = 1 orientifold compactifications Thomas W. Grimm University of Wisconsin, Madison based on: [hep-th/0602241] Iman Benmachiche, TWG [hep-th/0507153] TWG Madison, Wisconsin, November 2006
More informationCalabi-Yau Fourfolds with non-trivial Three-Form Cohomology
Calabi-Yau Fourfolds with non-trivial Three-Form Cohomology Sebastian Greiner arxiv: 1512.04859, 1702.03217 (T. Grimm, SG) Max-Planck-Institut für Physik and ITP Utrecht String Pheno 2017 Sebastian Greiner
More informationDavid R. Morrison. String Phenomenology 2008 University of Pennsylvania 31 May 2008
: : University of California, Santa Barbara String Phenomenology 2008 University of Pennsylvania 31 May 2008 engineering has been a very successful approach to studying string vacua, and has been essential
More informationSome Issues in F-Theory Geometry
Outline Some Issues in F-Theory Geometry Arthur Hebecker (Heidelberg) based on work with A. Braun, S. Gerigk, H. Triendl 0912.1596 A. Braun, R. Ebert, R. Valandro 0907.2691 as well as two earlier papers
More informationNew Toric Swiss Cheese Solutions
String Phenomenology 2017 (Based on arxiv:1706.09070 [hep-th]) Northeastern University 1/31 Outline Motivation 1 Motivation 2 CY Geometry Large Volume Scenario 3 Explicit Toric 4 2/31 Abundance of Moduli
More informationMagdalena Larfors. New Ideas at the Interface of Cosmology and String Theory. UPenn, Ludwig-Maximilians Universität, München
Ludwig-Maximilians Universität, München New Ideas at the Interface of Cosmology and String Theory UPenn, 17.03.01. String 10D supergravity M 10 = M 4 w M 6 Fluxes and branes... (Scientific American) Topology
More informationInflation in String Theory. mobile D3-brane
Inflation in String Theory mobile D3-brane Outline String Inflation as an EFT Moduli Stabilization Examples of String Inflation Inflating with Branes Inflating with Axions (Inflating with Volume Moduli)
More informationFlux Compactification of Type IIB Supergravity
Flux Compactification of Type IIB Supergravity based Klaus Behrndt, LMU Munich Based work done with: M. Cvetic and P. Gao 1) Introduction 2) Fluxes in type IIA supergravity 4) Fluxes in type IIB supergravity
More informationF-term Moduli Stabilization and Uplifting
EPHOU-18-015 KUNS-744 MISC-018- arxiv:181.0376v1 hep-th] 6 Dec 018 F-term Moduli Stabilization and Uplifting Tatsuo Kobayashi 1, Osamu Seto,1, Shintaro Takada 1, Takuya H. Tatsuishi 1, Shohei Uemura 3,
More informationarxiv:hep-th/ v2 28 Mar 2000
PUPT-1923 arxiv:hep-th/0003236v2 28 Mar 2000 A Note on Warped String Compactification Chang S. Chan 1, Percy L. Paul 2 and Herman Verlinde 1 1 Joseph Henry Laboratories, Princeton University, Princeton
More informationCandidates for Inflation in Type IIB/F-theory Flux Compactifications
Candidates for Inflation in Type IIB/F-theory Flux Compactifications Irene Valenzuela IFT UAM/CSIC Madrid Geometry and Physics of F-Theory, Munich 2015 Garcia-Etxebarria,Grimm,Valenzuela [hep-th/1412.5537]
More informationAn up-date on Brane Inflation. Dieter Lüst, LMU (Arnold Sommerfeld Center) and MPI für Physik, München
An up-date on Brane Inflation Dieter Lüst, LMU (Arnold Sommerfeld Center) and MPI für Physik, München Leopoldina Conference, München, 9. October 2008 An up-date on Brane Inflation Dieter Lüst, LMU (Arnold
More informationString Theory Compactifications with Background Fluxes
String Theory Compactifications with Background Fluxes Mariana Graña Service de Physique Th Journées Physique et Math ématique IHES -- Novembre 2005 Motivation One of the most important unanswered question
More informationCounting black hole microstates as open string flux vacua
Counting black hole microstates as open string flux vacua Frederik Denef KITP, November 23, 2005 F. Denef and G. Moore, to appear Outline Setting and formulation of the problem Black hole microstates and
More informationNovel potentials for string axion inflation
Novel potentials for string axion inflation 1. Introduction Tatsuo Kobayashi. Threshold corrections: Dedekind eta function 3. Quantum corrected period vector 4. Summary Abe, T.K., Otsuka, arxiv:1411.4768
More informationMagdalena Larfors
Uppsala University, Dept. of Theoretical Physics Based on D. Chialva, U. Danielsson, N. Johansson, M.L. and M. Vonk, hep-th/0710.0620 U. Danielsson, N. Johansson and M.L., hep-th/0612222 2008-01-18 String
More informationBasic Results in Vacuum Statistics
Basic Results in Vacuum Statistics Michael R. Douglas Rutgers and I.H.E.S. Strings 2004, Paris Abstract Based on hep-th/0303194, hep-th/0405279 and hep-th/0307049 with Sujay Ashok math.cv/0402326 with
More informationA Landscape of Field Theories
A Landscape of Field Theories Travis Maxfield Enrico Fermi Institute, University of Chicago October 30, 2015 Based on arxiv: 1511.xxxxx w/ D. Robbins and S. Sethi Summary Despite the recent proliferation
More informationFlux Compactification and SUSY Phenomenology
Flux Compactification and SUSY Phenomenology Komaba07 On occasion of Prof. Yoneya s 60 th birthday Masahiro Yamaguchi Tohoku University Talk Plan Introduction : Flux compactification and KKLT set-up Naturalness
More information2 Type IIA String Theory with Background Fluxes in d=2
2 Type IIA String Theory with Background Fluxes in d=2 We consider compactifications of type IIA string theory on Calabi-Yau fourfolds. Consistency of a generic compactification requires switching on a
More informationMIFPA PiTP Lectures. Katrin Becker 1. Department of Physics, Texas A&M University, College Station, TX 77843, USA. 1
MIFPA-10-34 PiTP Lectures Katrin Becker 1 Department of Physics, Texas A&M University, College Station, TX 77843, USA 1 kbecker@physics.tamu.edu Contents 1 Introduction 2 2 String duality 3 2.1 T-duality
More informationHeterotic Torsional Backgrounds, from Supergravity to CFT
Heterotic Torsional Backgrounds, from Supergravity to CFT IAP, Université Pierre et Marie Curie Eurostrings@Madrid, June 2010 L.Carlevaro, D.I. and M. Petropoulos, arxiv:0812.3391 L.Carlevaro and D.I.,
More informationRealistic D-Brane Models on Warped Throats: Fluxes, Hierarchies and Moduli Stabilization
Preprint typeset in JHEP style - HYPER VERSION DAMTP-2003-133 IFT-UAM/CSIC-03-50 FTUAM-03-28 hep-th/0312051 arxiv:hep-th/0312051v2 10 Dec 2003 Realistic D-Brane Models on Warped Throats: Fluxes, Hierarchies
More informationIssues in Type IIA Uplifting
Preprint typeset in JHEP style - HYPER VERSION hep-th/0612057 SU-ITP-2006-34 SLAC-PUB-12251 December 7, 2006 Issues in Type IIA Uplifting Renata Kallosh a and Masoud Soroush a,b a Department of Physics,
More informationModuli stabilization
Valerie Domcke June 28, 2011 oduli stabilization Abstract etric moduli generically arise in theories with extra dimensions. If not stabilized by some mechanism, these massless scalar fields can cause serious
More informationTopological String Theory
Topological String Theory Hirosi Ooguri (Caltech) Strings 2005, Toronto, Canada If String Theory is an answer, what is the question? What is String Theory? If Topological String Theory is an answer, what
More informationPatterns of supersymmetry breaking in moduli-mixing racetrack model
13 June, 2006 @ SUSY 06, UC Irvine Patterns of supersymmetry breaking in moduli-mixing racetrack model Based on articles Hiroyuki Abe (YITP, Kyoto) Phys.Rev.D73 (2006) 046005 (hep-th/0511160) Nucl.Phys.B742
More informationHeterotic type IIA duality with fluxes and moduli stabilization
Heterotic type IIA duality with fluxes and moduli stabilization Andrei Micu Physikalisches Institut der Universität Bonn Based on hep-th/0608171 and hep-th/0701173 in collaboration with Jan Louis, Eran
More informationCosmology with Extra Dimensions
Cosmology with Extra Dimensions Johannes Martin University of Bonn May 13th 2005 Outline Motivation and Introduction 1 Motivation and Introduction Motivation From 10D to 4D: Dimensional Reduction Common
More informationString cosmology and the index of the Dirac operator
String cosmology and the index of the Dirac operator Renata Kallosh Stanford STRINGS 2005 Toronto, July 12 Outline String Cosmology, Flux Compactification,, Stabilization of Moduli, Metastable de Sitter
More informationHeterotic Geometry and Fluxes
Heterotic Geometry and Fluxes Li-Sheng Tseng Abstract. We begin by discussing the question, What is string geometry? We then proceed to discuss six-dimensional compactification geometry in heterotic string
More informationKähler Potentials for Chiral Matter in Calabi-Yau String Compactifications
Kähler Potentials for Chiral Matter in Calabi-Yau String Compactifications Joseph P. Conlon DAMTP, Cambridge University Kähler Potentials for Chiral Matter in Calabi-Yau String Compactifications p. 1/4
More informationNon-Geometric Calabi- Yau Backgrounds
Non-Geometric Calabi- Yau Backgrounds CH, Israel and Sarti 1710.00853 A Dabolkar and CH, 2002 Duality Symmetries Supergravities: continuous classical symmetry, broken in quantum theory, and by gauging
More informationKähler Potentials for Chiral Matter in Calabi-Yau String Compactifications
Kähler Potentials for Chiral Matter in Calabi-Yau String Compactifications Joseph P. Conlon DAMTP, Cambridge University Kähler Potentials for Chiral Matter in Calabi-Yau String Compactifications p. 1/4
More informationString Theory. A general overview & current hot topics. Benjamin Jurke. Würzburg January 8th, 2009
String Theory A general overview & current hot topics Benjamin Jurke 4d model building Non-perturbative aspects Optional: Vafa s F-theory GUT model building Würzburg January 8th, 2009 Compactification
More informationIII. Stabilization of moduli in string theory II
III. Stabilization of moduli in string theory II A detailed arguments will be given why stabilization of certain moduli is a prerequisite for string cosmology. New ideas about stabilization of moduli via
More informationBrane world scenarios
PRAMANA cfl Indian Academy of Sciences Vol. 60, No. 2 journal of February 2003 physics pp. 183 188 Brane world scenarios DILEEP P JATKAR Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad
More informationSoft Supersymmetry Breaking Terms in String Compactifications
Soft Supersymmetry Breaking Terms in String Compactifications Joseph P. Conlon DAMTP, Cambridge University Soft Supersymmetry Breaking Terms in String Compactifications p. 1/4 This talk is based on hep-th/0609180
More informationBobby Samir Acharya Kickoff Meeting for Simons Collaboration on Special Holonomy
Particle Physics and G 2 -manifolds Bobby Samir Acharya Kickoff Meeting for Simons Collaboration on Special Holonomy King s College London µf µν = j ν dϕ = d ϕ = 0 and ICTP Trieste Ψ(1 γ 5 )Ψ THANK YOU
More informationDualities and Topological Strings
Dualities and Topological Strings Strings 2006, Beijing - RD, C. Vafa, E.Verlinde, hep-th/0602087 - work in progress w/ C. Vafa & C. Beasley, L. Hollands Robbert Dijkgraaf University of Amsterdam Topological
More informationG 2 manifolds and mirror symmetry
G 2 manifolds and mirror symmetry Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics First Annual Meeting, New York, 9/14/2017 Andreas Braun University of Oxford based on [1602.03521]
More informationOn Acceleration of the Universe. Waseda University Kei-ichi Maeda
On Acceleration of the Universe Waseda University Kei-ichi Maeda Acceleration of cosmic expansion Inflation: early stage of the Universe Inflaton? Present Acceleration cosmological constant Dark Energy
More informationOrientiholes Γ 2 Γ 1. Frederik Denef, Mboyo Esole and Megha Padi, arxiv:
Orientiholes Γ 2 Γ 1 Γ 0 Γ 1 Γ 2 Frederik Denef, Mboyo Esole and Megha Padi, arxiv:0901.2540 Outline Motivation and basic idea Review of N = 2 black hole bound states Type IIA orientiholes Motivation and
More informationKähler Potentials for Chiral Matter in Calabi-Yau String Compactifications
Kähler Potentials for Chiral Matter in Calabi-Yau String Compactifications Joseph P. Conlon DAMTP, Cambridge University Kähler Potentials for Chiral Matter in Calabi-Yau String Compactifications p. 1/3
More informationString Theory in a Nutshell. Elias Kiritsis
String Theory in a Nutshell Elias Kiritsis P R I N C E T O N U N I V E R S I T Y P R E S S P R I N C E T O N A N D O X F O R D Contents Preface Abbreviations xv xvii Introduction 1 1.1 Prehistory 1 1.2
More informationInflation in heterotic supergravity models with torsion
Inflation in heterotic supergravity models with torsion Stephen Angus IBS-CTPU, Daejeon in collaboration with Cyril Matti (City Univ., London) and Eirik Eik Svanes (LPTHE, Paris) (work in progress) String
More informationCalabi-Yau Spaces in String Theory
Habilitationsschrift Calabi-Yau Spaces in String Theory Johanna Knapp Institut fu r Theoretische Physik Technische Universita t Wien Wiedner Hauptstraße 8-0 040 Wien O sterreich Wien, September 05 Abstract
More informationHierarchy Problems in String Theory: An Overview of the Large Volume Scenario
Hierarchy Problems in String Theory: An Overview of the Large Volume Scenario Joseph P. Conlon (Cavendish Laboratory & DAMTP, Cambridge) Stockholm, February 2008 Hierarchy Problems in String Theory: An
More informationFluxes, branes and black holes - how to find the right string vacuum?
Fluxes, branes and black holes - how to find the right string vacuum? Dieter Lüst, LMU (ASC) and MPI München in collaboration with Ralph Blumenhagen, Gabriel L. Cardoso, Florian Gmeiner, Daniel Krefl,
More informationOpen Office (Linux) A String Manifesto. Marcus Berg CoPS. M.B., Haack, Pajer '07 M.B., Haack, Körs '05, '04
Open Office (Linux) A String Manifesto Marcus Berg CoPS M.B., Haack, Pajer '07 M.B., Haack, Körs '05, '04 Open Office (Linux) A String Manifesto Marcus Berg CoPS Summary of current state of affairs Statement
More informationPietro Fre' SISSA-Trieste. Paolo Soriani University degli Studi di Milano. From Calabi-Yau manifolds to topological field theories
From Calabi-Yau manifolds to topological field theories Pietro Fre' SISSA-Trieste Paolo Soriani University degli Studi di Milano World Scientific Singapore New Jersey London Hong Kong CONTENTS 1 AN INTRODUCTION
More informationPhenomenological Aspects of Local String Models
Phenomenological Aspects of Local String Models F. Quevedo, Cambridge/ICTP. PASCOS-2011, Cambridge. M. Dolan, S. Krippendorf, FQ; arxiv:1106.6039 S. Krippendorf, M. Dolan, A. Maharana, FQ; arxiv:1002.1790
More informationKnot Homology from Refined Chern-Simons Theory
Knot Homology from Refined Chern-Simons Theory Mina Aganagic UC Berkeley Based on work with Shamil Shakirov arxiv: 1105.5117 1 the knot invariant Witten explained in 88 that J(K, q) constructed by Jones
More informationLecture Notes on D-brane Models with Fluxes
Max-Planck-Institut für Physik, Föhringer Ring 6, D-80805 München, GERMANY E-mail: blumenha@mppmu.mpg.de This is a set of lecture notes for the RTN Winter School on Strings, Supergravity and Gauge Theories,
More informationWhat is F-theory? David R. Morrison. University of California, Santa Barbara
University of California, Santa Barbara Physics and Geometry of F-theory 2015 Max Plack Institute for Physics, Munich 25 February 2015 arxiv:1503.nnnnn Inspired in part by Grassi Halverson Shaneson arxiv:1306.1832
More informationSCFTs, Compact CY 3-folds, and Topological Strings
SCFTs, Compact CY 3-folds, and Topological Strings Patrick Jefferson (to appear) in collaboration with: Hirotaka Hayashi, Hee-Cheol Kim, Kantaro Ohmori, and Cumrun Vafa This subject of this talk is SCFTs
More informationTHE MASTER SPACE OF N=1 GAUGE THEORIES
THE MASTER SPACE OF N=1 GAUGE THEORIES Alberto Zaffaroni CAQCD 2008 Butti, Forcella, Zaffaroni hepth/0611229 Forcella, Hanany, Zaffaroni hepth/0701236 Butti,Forcella,Hanany,Vegh, Zaffaroni, arxiv 0705.2771
More informationWeb of threefold bases in F-theory and machine learning
and machine learning 1510.04978 & 1710.11235 with W. Taylor CTP, MIT String Data Science, Northeastern; Dec. 2th, 2017 1 / 33 Exploring a huge oriented graph 2 / 33 Nodes in the graph Physical setup: 4D
More informationBrane Backreaction: antidote to no-gos
Brane Backreaction: antidote to no-gos Getting de Sitter (and flat) space unexpectedly w Leo van Nierop Outline New tool: high codim back-reaction RS models on steroids Outline New tool: high codim back-reaction
More informationMirrored K3 automorphisms and non-geometric compactifications
Mirrored K3 automorphisms and non-geometric compactifications Dan Israe l, LPTHE New Frontiers in String Theory, Kyoto 2018 Based on: D.I. and Vincent Thie ry, arxiv:1310.4116 D.I., arxiv:1503.01552 Chris
More informationLooking Beyond Complete Intersection Calabi-Yau Manifolds. Work in progress with Hans Jockers, Joshua M. Lapan, Maurico Romo and David R.
Looking Beyond Complete Intersection Calabi-Yau Manifolds Work in progress with Hans Jockers, Joshua M. Lapan, Maurico Romo and David R. Morrison Who and Why Def: X is Calabi-Yau (CY) if X is a Ricci-flat,
More informationFrom Flux Compactification to Cosmology
From Flux Compactification to Cosmology Xin Gao Virginia Tech & ITP-CAS CTP-SCU, 3 July, 2014 The Road to Unification Overview of String Theory Outline Flux Compactifications Calabi-Yau and its Moduli
More informationGood things from Brane Backreaction
Good things from Brane Backreaction Codimension-2 Backreaction as a counterexample to almost everything w Leo van Nierop Outline New tool: high codim back-reaction RS models on steroids Outline New tool:
More informationStrings and the Cosmos
Strings and the Cosmos Yeuk-Kwan Edna Cheung Perimeter Institute for Theoretical Physics University of Science and Technology, China May 27th, 2005 String Theory as a Grand Unifying Theory 60 s: theory
More informationElements of Topological M-Theory
Elements of Topological M-Theory (with R. Dijkgraaf, S. Gukov, C. Vafa) Andrew Neitzke March 2005 Preface The topological string on a Calabi-Yau threefold X is (loosely speaking) an integrable spine of
More informationString Phenomenology ???
String Phenomenology Andre Lukas Oxford, Theoretical Physics d=11 SUGRA IIB M IIA??? I E x E 8 8 SO(32) Outline A (very) basic introduction to string theory String theory and the real world? Recent work
More informationMirror symmetry for G 2 manifolds
Mirror symmetry for G 2 manifolds based on [1602.03521] [1701.05202]+[1706.xxxxx] with Michele del Zotto (Stony Brook) 1 Strings, T-duality & Mirror Symmetry 2 Type II String Theories and T-duality Superstring
More informationN=2 Supergravity D-terms, Cosmic Strings and Brane Cosmologies
N=2 Supergravity D-terms, Cosmic Strings and Brane Cosmologies Antoine Van Proeyen K.U. Leuven Paris, 30 years of Supergravity, 20 October 2006 Supergravity for string cosmology Since a few years there
More informationFixing All Moduli for M-Theory on K3 x K3
Fixing All Moduli for M-Theory on K3 x K3 Renata Kallosh Stanford Superstring Phenomenology 2005, Munich June 16 Aspinwall, R. K. hep-th/0506014 R.K., Kashani-Poor, Tomasiello, hep-th/0503138 Bergshoeff,
More informationSupersymmetric Standard Models in String Theory
Supersymmetric Standard Models in String Theory (a) Spectrum (b) Couplings (c) Moduli stabilisation Type II side [toroidal orientifolds]- brief summary- status (a),(b)&(c) Heterotic side [Calabi-Yau compactification]
More informationDisk Instantons, Mirror Symmetry and the Duality Web
HUTP-01/A023 HU-EP-01/21 hep-th/0105045 Disk Instantons, Mirror Symmetry and the Duality Web Mina Aganagic 1, Albrecht Klemm 2 and Cumrun Vafa 1 1 Jefferson Physical Laboratory Harvard University, Cambridge,
More informationTopological reduction of supersymmetric gauge theories and S-duality
Topological reduction of supersymmetric gauge theories and S-duality Anton Kapustin California Institute of Technology Topological reduction of supersymmetric gauge theories and S-duality p. 1/2 Outline
More informationFlux vacua in String Theory, generalized calibrations and supersymmetry breaking. Luca Martucci
Flux vacua in String Theory, generalized calibrations and supersymmetry breaking Luca Martucci Workshop on complex geometry and supersymmetry, IPMU January 4-9 2009 Plan of this talk Generalized calibrations
More informationarxiv: v2 [hep-th] 3 Jul 2015
Prepared for submission to JHEP NSF-KITP-15-068, MIT-CTP-4677 P 1 -bundle bases and the prevalence of non-higgsable structure in 4D F-theory models arxiv:1506.03204v2 [hep-th] 3 Jul 2015 James Halverson
More informationBranes in Flux Backgrounds and Dualities
Workshop on recent developments in string effective actions and D-instantons Max-Planck-Institute fur Physik, Munich Branes in Flux Backgrounds and Dualities Giovanni Villadoro Harvard University based
More informationHeterotic Flux Compactifications
Heterotic Flux Compactifications Mario Garcia-Fernandez Instituto de Ciencias Matemáticas, Madrid String Pheno 2017 Virginia Tech, 7 July 2017 Based on arxiv:1611.08926, and joint work with Rubio, Tipler,
More informationD-brane instantons in Type II orientifolds
D-brane instantons in Type II orientifolds in collaboration with R. Blumenhagen, M. Cvetič, D. Lüst, R. Richter Timo Weigand Department of Physics and Astronomy, University of Pennsylvania Strings 2008
More informationModuli stabilization and supersymmetry breaking for string phenomenology
Moduli stabilization and supersymmetry breaking for string phenomenology Tetsutaro Higaki (DESY) Based on works with Hiroyuki Abe, Ryuichiro Kitano, Tatsuo Kobayashi, Yuji Omura and Osamu Seto Why moduli?
More informationarxiv:hep-th/ v3 25 Aug 1999
TIT/HEP-411 arxiv:hep-th/9904155v3 25 Aug 1999 Puzzles on the Duality between Heterotic and Type IIA Strings Mitsuko Abe and Masamichi Sato Department of Physics Tokyo Institute of Technology Oh-okayama,
More informationString Moduli Stabilization and Large Field Inflation
Kyoto, 12.12.2016 p.1/32 String Moduli Stabilization and Large Field Inflation Ralph Blumenhagen Max-Planck-Institut für Physik, München based on joint work with A.Font, M.Fuchs, D. Herschmann, E. Plauschinn,
More informationExploring the Kähler potential
Exploring the Michael R. Douglas Rutgers and IHES Strings 2007, Madrid Abstract Based on hep-th/0606261, 0704.4001 and to appear with: Robert Karp Semen Klevtsov Sergio Lukic Rene Reinbacher Jessie Shelton
More informationNon-Kähler Calabi-Yau Manifolds
Non-Kähler Calabi-Yau Manifolds Shing-Tung Yau Harvard University String-Math 2011 University of Pennsylvania June 6, 2011 String and math have had a very close interaction over the past thirty years.
More informationTopological Holography and Chiral Algebras. Work in progress with Kevin Costello
Topological Holography and Chiral Algebras Work in progress with Kevin Costello General Motivations Topological twist of sugra/superstrings as holographic dual of twisted SQFT (Costello) Topological Holography:
More informationAn introduction to heterotic mirror symmetry. Eric Sharpe Virginia Tech
An introduction to heterotic mirror symmetry Eric Sharpe Virginia Tech I ll begin today by reminding us all of ordinary mirror symmetry. Most basic incarnation: String theory on a Calabi-Yau X = String
More informationWrapped brane gas as a candidate for Dark Matter
Wrapped brane gas as a candidate for Dark Matter Masakazu Sano Hokkaido University arxiv:0907.2495 in collaboration with Hisao Suzuki KEK Mini Workshop on String Theory, 09 Nov, 2009 1 Introduction Table
More informationSolution Set 8 Worldsheet perspective on CY compactification
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics String Theory (8.821) Prof. J. McGreevy Fall 2007 Solution Set 8 Worldsheet perspective on CY compactification Due: Monday, December 18, 2007
More informationCosmology of moving branes and spinflation
Cosmology of moving branes and spinflation 8 Dark Energy in the Universe Damien Easson University of Tokyo Outline Brane Inflation, Moduli Stabilization and Flux Compactifications Cyclic, Mirage cosmologies
More informationKnots and Mirror Symmetry. Mina Aganagic UC Berkeley
Knots and Mirror Symmetry Mina Aganagic UC Berkeley 1 Quantum physics has played a central role in answering the basic question in knot theory: When are two knots distinct? 2 Witten explained in 88, that
More informationFabio Riccioni. 17th July 2018 New Frontiers in String Theory 2018 Yukawa Institute for Theoretical Physics, Kyoto
& & 17th July 2018 New Frontiers in String Theory 2018 Yukawa Institute for Theoretical Physics, Kyoto Based on arxiv:1803.07023 with G. Dibitetto and S. Risoli arxiv:1610.07975, 1704.08566 with D. Lombardo
More informationOn Special Geometry of Generalized G Structures and Flux Compactifications. Hu Sen, USTC. Hangzhou-Zhengzhou, 2007
On Special Geometry of Generalized G Structures and Flux Compactifications Hu Sen, USTC Hangzhou-Zhengzhou, 2007 1 Dreams of A. Einstein: Unifications of interacting forces of nature 1920 s known forces:
More informationBrane inflation in string cosmology. Shinji Mukohyama (University of Tokyo) based on collaboration with S.Kinoshita, T.Kobayashi, L.
Brane inflation in string cosmology Shinji Mukohyama (University of Tokyo) based on collaboration with S.Kinoshita, T.Kobayashi, L.Kofman Three mysteries: Inflation, Dark Energy & Dark Matter String Theory?
More informationarxiv: v1 [hep-th] 12 Oct 2007
CHERN CLASS IDENTITIES FROM TADPOLE MATCHING IN TYPE IIB AND F-THEORY PAOLO ALUFFI AND MBOYO ESOLE arxiv:0710.2544v1 [hep-th] 12 Oct 2007 Abstract. In light of Sen s weak coupling limit of F-theory as
More informationDisk Instantons, Mirror Symmetry and the Duality Web
Disk Instantons, Mirror Symmetry and the Duality Web Mina Aganagic, Albrecht Klemm a, and Cumrun Vafa Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA a Institut für Physik,
More informationD-branes in non-abelian gauged linear sigma models
D-branes in non-abelian gauged linear sigma models Johanna Knapp Vienna University of Technology Bonn, September 29, 2014 Outline CYs and GLSMs D-branes in GLSMs Conclusions CYs and GLSMs A Calabi-Yau
More information