Progress in Warped String Compactifications Gary Shiu University - PowerPoint PPT Presentation

Progress in Warped String Compactifications Gary Shiu University of Wisconsin

Collaborators • D-brane Inflation & Non-Gaussianities in CMB: Bret Underwood, Steven Kecskemeti, John Maiden, Diego Chialva, Xingang Chen, Min-xin Huang, Shamit Kachru • Warped Throats at the LHC: Bret Underwood, Devin Walker, Kathryn Zurek • D3-brane vacua in Stabilized Compactifications: Oliver DeWolfe, Liam McAllister, Bret Underwood • Dynamics of Warped Flux Compactifications: Michael Douglas, Gonzalo Torroba, Bret Underwood

Collaborators • D-brane Inflation & Non-Gaussianities in CMB: Bret Underwood, Steven Kecskemeti, John Maiden, Diego Chialva, Xingang Chen, Min-xin Huang, Shamit Kachru • Warped Throats at the LHC: Bret Underwood, Devin Walker, Kathryn Zurek • D3-brane vacua in Stabilized Compactifications: Oliver DeWolfe, Liam McAllister, Bret Underwood • Dynamics of Warped Flux Compactifications: Michael Douglas, Gonzalo Torroba, Bret Underwood

Warped String Vacua: Open String Sector A Gentle Landscape

A Warped Landscape

Motivation

Motivation Stabilizing moduli

Motivation Stabilizing moduli String Inflation

Warped String Inflation • Warping invoked in slow-roll & DBI inflation models. • CMB Signatures depend strongly on geometries. η KS Mass Gap N e AdS N tot Baumann, Dymarsky, Klebanov, GS, Underwood McAllister, Steinhardt

Non-Gaussianities • Models with large non-Gaussianities & distinctive shape. Alishahiha, Silverstein, Tong • Exact numerical factors and shape for general single field inflation computed. Chen, Huang, Kachru, GS [See also: Cheung, Cremenini, Fitzpatrick, Kaplan, Senatore] � ζ k 1 ζ k 2 ζ k 3 � = (2 π ) 3 δ 3 ( k 1 + k 2 + k 3 ) F ( k 1 , k 2 , k 3 ) f NL ∼ O ( � ) Slow-roll f NL ∼ O ( γ 2 ) DBI k2 k3 [See talks of Shandera, Leblond, ...] F (1 , k 2 , k 3 ) k 2 2 k 2 3

Motivation Stabilizing moduli Inflation RS-like hierarchy

Hierarchy from Warping Giddings, Kachru, Polchinski; KKLT; Dasgupta, Rajesh, Sethi; ... Scale of inflation, electroweak scale, ... KS AdS GS, Underwood, Walker, Zurek

Motivation Stabilizing moduli String Inflation RS-like hierarchy

Motivation Scale of SUSY Stabilizing moduli mediation scenario, sequestering, ... String Local model: Inflation explicit metric RS-like Gauge/gravity Cosmic strings, hierarchy correspondence reheating, ...

Warped Effective Theory V 0.2 Douglas, Shelton,Torroba 0.15 0.1 0.05 S 0.5 1 1.5 2 • Finding vacua & fluctuations around • Flatness of inflaton potential Require warping corrections to • Computation of soft SUSY terms N=1, D=4 SUGRA • ...

Warped String Vacua 1. Open String Sector DeWolfe, McAllister, GS, Underwood 2. Closed String Sector GS, Torroba, Underwood, Douglas

Warped String Vacua 1. Open String Sector DeWolfe, McAllister, GS, Underwood 2. Closed String Sector GS, Torroba, Underwood, Douglas (STUD)

Warped String Vacua: Open String Sector DeWolfe, McAllister, GS, Underwood

D-BRANE MODULI D-brane models of particle physics Talks of Vafa, Verlinde, Wijnholt, ... F-theory/open string landscape Gomis, Marchesano, Mateos; Collinucci, Denef, Esole; ... End of brane-inflation, reheating Barnaby, Burgess, Cline; Kofman, Yi; Chialva, GS, Underwood; Frey, Mazumdar, Myers; Chen,Tye; ... Multi-field effects in brane inflation Huang, GS, Underwood; Easson et al; Shandera, Leblond; ... ....

Multifield Effects of D-brane Inflation D3-brane has angular coordinates: multi-field inflation Huang, GS, Underwood; [See also Easson et al] Multi-field DBI inflation: interesting and significant effects on non-Gaussianities Langlois, Renaux-Petel, Steer, Tanaka Entropy Curvature perturbations perturbations Transfer function: T RS depends on sharpness of turn, (weakly broken) isometry directions, ...

Type IIB Flux Compactifications Metric is warped product of 4d with (conformally) CY Fluxes Instantons D7 or Euclidean D3 Generate warping & stabilize Stabilize Kahler moduli. complex structure moduli. KKLT, ... GKP; Dasgupta, Rajesh, Sethi, ... Stabilize D7 positions. Stabilize D3 positions.

Warped Deformed Conifold Geometry of KS throat: • Approximately AdS 5 xT 1,1 far from tip • Topologically • Finite size S 3 at tip

Warped Deformed Conifold Geometry of KS throat: • Approximately AdS 5 xT 1,1 far from tip • Topologically • Finite size S 3 at tip Before KKLT effects, D3 moduli space = M 6

D3 Moduli Stabilization D7 branes wrapped on Σ 4 Backreaction of D3 on V ol (Σ 4 ) Baumann, Dymarsky, Klebanov, Maldacena, McAllister, Murugan; [See also Berg, Haack, Kors; Giddings, Maharana; Ganor] D3 pushed to the tip by D7-brane

D3 Moduli Stabilization D7 branes wrapped on Σ 4 Backreaction of D3 on V ol (Σ 4 ) Baumann, Dymarsky, Klebanov, Maldacena, McAllister, Murugan; [See also Berg, Haack, Kors; Giddings, Maharana; Ganor] D3 vacua depend on 4-cycle embeddings D3 pushed to the tip by D7-brane

D3 Moduli Stabilization D7 branes wrapped on Σ 4 Backreaction of D3 on V ol (Σ 4 ) Baumann, Dymarsky, Klebanov, Maldacena, McAllister, Murugan; [See also Berg, Haack, Kors; Giddings, Maharana; Ganor] D3 vacua depend on break throat 4-cycle embeddings isometries D3 pushed to the tip by D7-brane

Wrapped Branes in Throats Deformed conifold coordinates: Embedding of D7 defined by a holomorphic function: •ACR or Ouyang-type Arean, Crooks, Ramallo Karch, Katz P. Ouyang •Kuperstein-type S. Kuperstein

SUSY Flavor Branes Flavor branes defined by holomorphic functions: f ( z ) = 0 or f ( w ) = 0 κ symmetry requires further that: F = ˆ ˆ F 2 , 0 = ˆ F 0 , 2 = 0 . ˆ B 2 + 2 πα ′ F , � e 2 A � J − 1 e − A ˆ J ∧ ˆ J ∧ ˆ ˆ F ∧ ˆ ˆ Marino, Minasian, Moore, Strominger F = tan θ F 2 2 only been checked for the Kuperstein embedding. Naively not satisfied for other embeddings, but field theory dual has SUSY moduli space in IR. Explicit construction of F H.-Y. Chen, Ouyang, GS (in progress)

D3 Vacua in KS Throat DeWolfe, McAllister, GS, Underwood Using the DG Kahler potential (later): ρ K = − 3 log e 4 u = − 3 log( ρ + ¯ ρ − γk ( Y, ¯ Y ) / 3) W np and above. Solve F-term equations: D3 generically stabilized at pts D3 vacua on S 3 : pushes away from D7

D3 vacua in KS Throat Deformed conifold coordinates: 4 z A � 2 = − 2 ( w 1 w 2 − w 3 w 4 ) = � 2 � � A =1 General ACR-type: Ouyang-type: Kuperstein-type: Preserves No SUSY D3 vacua! D3 stabilized at points Isometry further broken weakly by bulk effects. DeWolfe, McAllister, GS, Underwood

Warped String Vacua: Closed String Sector GS, Torroba, Underwood, Douglas (STUD)

Issues with Strong Warping D=10 String Theory Ex: GKP and KKLT Type IIB String Theory in D=10 Low Energy Low Energy D=10 SUGRA IIB Supergravity in D=10 with fluxes KK Dimensional KK Reduction Dimensional Reduction D=4 N=1 N =1 SUGRA in D=4 SUGRA EFT String vacua, inflation, de-Sitter, MSSM…

Issues with Strong Warping D=10 String Theory Low Energy Many subtleties with warped KK reduction: D=10 SUGRA • General KK ansatz (compensators) with fluxes • Mixing/sourcing of KK modes with moduli KK • Backreaction of moduli on warp factor Dimensional Reduction • 10D Gauge redundancies D=4 N=1 • 10D Constraint equations SUGRA EFT In warped backgrounds these issues are all highly coupled to each other! String vacua, inflation, de-Sitter, MSSM…

KK Scale in Warped Background Moduli KK modes z ∼ 1 m 2 Unwarped α �

KK Scale in Warped Background Moduli KK modes z ∼ 1 m 2 Unwarped α � DeWolfe, Giddings; Giddings, Maharana; Strong warping Frey, Maharana; Burgess, Camara, de Alwis, Giddings, Maharana, Quevedo, Suruliz; ...

KK Scale in Warped Background Moduli KK modes z ∼ 1 m 2 Unwarped α � DeWolfe, Giddings; Giddings, Maharana; Strong warping Frey, Maharana; Burgess, Camara, de Alwis, Giddings, Maharana, Quevedo, Fields localize to region of strong warping. Suruliz; ...

KK Scale in Warped Background Moduli KK modes z ∼ 1 m 2 Unwarped α � DeWolfe, Giddings; Giddings, Maharana; Strong warping Frey, Maharana; Burgess, Camara, de Alwis, Giddings, Maharana, Quevedo, Fields localize to region of strong warping. Suruliz; ... Masses redshifted

KK Scale in Warped Background Moduli KK modes z ∼ 1 m 2 Unwarped α � DeWolfe, Giddings; Giddings, Maharana; Strong warping Frey, Maharana; Burgess, Camara, de Alwis, Giddings, Maharana, Quevedo, Fields localize to region of strong warping. Suruliz; ... Masses redshifted No mass hierarchy between moduli and KK modes for integrating out heavy fields.

Towards a Warped EFT Previous proposals of 4D Warped EFT: DeWolfe, Giddings did not account for these issues. Ansatz for fluctuations: (DeWolfe, Giddings) ... does not solve 10D EOM! Giddings, Maharana; STUD More general ansatz does, but extremely messy ... Giddings, Maharana