On Vacuum Stability without Supersymmetry Brane dynamics, bubbles - PowerPoint PPT Presentation

On Vacuum Stability without Supersymmetry Brane dynamics, bubbles and holography Ivano Basile | SNS, Pisa | Cortona Young, May 2020 based on: • hep-th/1811.11448 with J. Mourad and A. Sagnotti • hep-th/1908.04352 with R. Antonelli • hep-th/1806.02289 with R. Antonelli and A. Bombini 1

[credits to Kurzgesagt ↑ ] 2

Non-SUSY 10d strings: vantage point? 1. Heterotic SO (16) × SO (16): NO SUSY (Alvarez–Gaume, Ginsparg, Moore, Vafa, 1986) 2. U (32) : Type 0’B closed + open : NO SUSY (Sagnotti, 1995) 3. USp (32) : closed + open (Sugimoto, 1999) “Brane SUSY Breaking” (Antoniadis, Dudas, Sagnotti, 1999) 10D couplings (Dudas, Mourad; Pradisi, Riccioni, 2000) Features • no tachyons • branes + orientifolds → residual tension V ( φ ) = V 0 e γ φ − → NO flat vacuum! • ∃ AdS × S flux backgrounds (Mourad, Sagnotti, 2016) are they stable? 3

Low-energy description � � � d 10 x √− g 2( ∂φ ) 2 − V ( φ ) − e αφ R − 1 12 H 2 S eff = 3 + . . . AdS flux compactifications: • Constant dilaton • AdS 3 × S 7 (BSB ≃ 0’B), AdS 7 × S 3 (heterotic) • electric vs magnetic flux N of H 3 = dB 2 e φ , ( α ′ R ) ≪ 1 N ≫ 1 − → 4

In orientifold models: AdS 3 × S 7 3 2 φ , coupling α = 1 to R-R 3-form Parameters : V = T e � 64 T D9 (BSB) from disk amplitude: T = 2 k 2 10 × 32 T D9 (0’B) • electric flux � S 7 ⋆ e φ H 3 N = • (super)gravity regime e φ ∝ N − 1 / 4 L 3 , R 7 ∝ N 3 / 16 • ratio of radii L 2 = 1 3 R 2 6 7 5

In the heterotic model: AdS 7 × S 3 5 2 φ , coupling α = − 1 to NS-NS 3-form Parameters : V = Λ e from 1-loop torus amplitude: Λ = (modular integral) = O (1) α ′ • magnetic flux � N = S 3 H 3 • (super)gravity regime e φ ∝ N − 1 / 2 L 7 , R 3 ∝ N 5 / 8 • ratio of radii L 2 7 = 12 R 2 3 6

Perturbative instabilities: Minkowski vs AdS m 2 < 0 → modes can grow AdS: BF bound (Breitenlohner, Freedman, 1982) scalar ≥ − ( d − 1) 2 m 2 4 L 2 AdS • some tachyons allowed! • extends to general fluctuations 7

Perturbative instabilities: results (IB, Mourad, Sagnotti, 2018) AdS vacua: unstable scalar KK modes AdS 3 × S 7 • BSB & 0’B − → ℓ = 2 , 3 , 4 AdS 7 × S 3 • Heterotic − → ℓ = 1 Dudas-Mourad vacua (Dudas, Mourad, 2000) : pert. stable... • 9d static: ...but large corrections • 10d cosmology: ...except isotropy? δ g ij ( k = 0) ∼ A ij + B ij log η 8

Non-perturbative instabilities expect instantons... B � �� � ( S inst. − S 0 ) Γ decay ∼ (det) × e − (Coleman, Callan, 1977), (Coleman, De Luccia, 1980) BUT: no global knowledge no SUSY! → any criteria? 9

Non-perturbative instabilities: brane picture (Antonelli, IB, 2019) AdS vacua → flux tunneling (Brown, Teitelboim, 1987-1988), (Blanco-Pillado, Schwartz-Perlov, Vilenkin, 2009) E vac ∝ − N − 3 − N − 2 or N − → N − δ N : out of EFT • Instantons ↔ branes (D1 or NS5)? right charge & dim. • AdS → near-horizon of brane stack... − → brane-antibrane nucleation � � N µ p S E brane = τ p Area − e αφ R q Vol = B CdL extremum 10

Consistency: the right branes � � 1 � p 1 − p + 1 u β 2 − 1 2 brane = τ p Ω p +1 L p +1 S E β √ 1 + u du ( β 2 − 1) p +1 2 2 0 Consistency: � µ p � − α • existence: nucl. parameter β ≡ v 0 g > 1 2 s τ p − α β = O ( N 0 ) − • semi-classical: → τ p = T p g 2 s − → relation for fundamental (and exotic) branes ! (Bergshoeff, Riccioni et al.) = T p σ = 1 + 1 2 α string τ string , p electric g σ s 11

After tunneling: Lorentzian evolution probe p / ¯ p -brane in (Poincar´ e) AdS throat at pos. Z : � L � p +1 � � µ p V probe = τ p 1 + − v 0 Z T p � charge � for our string models: v 0 > 1! WGC : ր ր tension eff − → these non-SUSY branes feel the right forces 12

Back-reaction: pinch-off at finite distance SO (1 , p ) × SO ( q ) geometry � √ g rr dr AdS p +2 × S q φ → ∞ φ = φ 0 S q � √ g rr dr < ∞ geodesic length: p = 8: recover 9d Dudas-Mourad 2 asymptotic free parameters: extremal tuning? 13

(Top-down) holography? Dual “CFT”: (IR of) world-volume gauge theory? c D1 ∝ N 3 / 2 Toward small N : bubble RG? Recent developments: “de Sitter on a brane”? (Banerjee, Danielsson, Dibitetto, Giri, Schillo, 2018) → Λ 6 d ∝ 1 e.g. N NS5-branes in SO (16) × SO (16) − N 2 14

AdS vacua: Flux tunneling: • weak coupling • vacuum bubbles • discrete ( N → g s , R ) • branes • non-SUSY • toward UV Brane picture • AdS ← → IR world-volume theory? • tunneling ← → renormalization group flows? • de Sitter on a brane? 15

Take-home message SUSY breaking spontaneous dynamics 16

Backup slides 17

Perturbations and mixings Linearized analysis: AdS tensors + angular momenta ℓ (IB, Mourad, Sagnotti, 2018) • Tensors: no mixing − → stable � • Vectors: mixing, still stable � δ g µ i δ B µ i • Scalars: Einstein eqs. − → 2 constraints! δφ δ B 2 = ⋆ 3 dB δ g µν = A g (0) µν δ g ij = C g (0) ij δ g µ i = ∇ µ ∇ i D 18

Linearized scalar equations: orientifold case � � 4 + 3 σ 3 + ℓ 3 A + 7 2 α σ 3 δφ − ℓ 3 L 2 3 � A − 3 ( σ 3 − 1) 2 ( σ 3 − 1) B = 0 � � 2 α 2 σ 3 + τ 3 + ℓ 3 δφ + α ℓ 3 L 2 3 � δφ + 2 α σ 3 A − 3 ( σ 3 − 1) 3 ( σ 3 − 1) B = 0 3 � B − 8 σ 3 A + 4 α σ 3 δφ − ℓ 3 L 2 3 ( σ 3 − 1) B = 0 where: σ 3 = 1 + 3 L 2 3 τ 3 = L 2 3 V ′′ ℓ 3 = ℓ ( ℓ + 6) , , 0 R 2 7 19

Linearized scalar equations: heterotic case 7 � A − [ ℓ 7 ( σ 7 − 3) + 5 σ 7 + 12] A + 5 2 α σ 7 δφ − 3 ℓ 7 L 2 2 ( σ 7 − 3) B = 0 � 2 α 2 σ 7 + τ 7 + ℓ 7 ( σ 7 − 3) � L 2 7 � δφ + 6 α σ 7 A − δφ + α ℓ 7 ( σ 7 − 3) B = 0 L 2 7 � B − 8 σ 7 A + 4 α σ 7 δφ − ℓ 7 ( σ 7 − 3) B = 0 where: σ 7 = 3 + L 2 7 τ 7 = L 2 7 V ′′ ℓ 7 = ℓ ( ℓ + 2) , , 0 R 2 3 20

Results: violations of BF bounds BSB Model 4 Scalars ( AdS 3 × S 7 ) BSB Model Vectors 3 • Scalars: ℓ = 2 , 3 , 4 2 • Vectors: ℓ = 1 massless (KK) 1 0 l ( AdS 7 × S 3 ) Heterotic Model 0 1 2 3 4 5 Heterotic Model • Scalars: ℓ = 1 Scalars 150 Vectors • Vectors: ℓ = 1 massless (KK) 100 50 Orbifolds: can get rid of unstable modes... → vacuum bubbles? (Horowitz, Orgera, Polchinski, 2008) 0 0 1 2 3 4 [also cosmological vacuum: stable, but isotropy breaking?] (IB, Mourad, Sagnotti, 2018) 21

Non-perturbative instabilities: flux tunneling • Gravity in D = p + 2 + q dims + fluxes: S q reduction ds 2 = R − 2 q p +2 + R 2 d Ω 2 p ds 2 q • Reduced action: ( p + 2)-Einstein frame � 1 � � � R p +2 − 2Λ R − 2 q d p +2 x S p +2 = − g p +2 p 2 κ 2 p +2 → E vac ∝ − R − 2 q p − 2 vacuum energy − E vac depends on flux... ...higher-dim. instantons, flux transitions (Blanco-Pillado, Schwartz-Perlov, Vilenkin, 2009) 22

Many branes: background geometry SO (1 , p ) × SO ( q ) symmetry: φ ( r ) , v ( r ) , b ( r ) ds 2 = e p +1 v − 2 q p b dx 2 1 , p + e 2 v − 2 q p b dr 2 + e 2 b R 2 2 0 d Ω 2 q , φ = φ ( r ) , N p ( p +2) b d p +1 x ∧ dr , H p +2 = c e 2 v − q c ≡ e αφ ( R 0 e b ) q (Constrained) Toda-like system: (+ , − , +) kinetic term w/ potential n 2 b + q ( q − 1) p b − e − αφ +2 v − 2 q ( p +1) e 2 v − 2( D − 2) U = − T e γφ +2 v − 2 q b p p 2 R 2 q R 2 0 0 23

Geometry: near-horizon Recover original AdS p +2 × S q with [ r < 0] � R � − q L 1 e b = R p e v = φ = φ 0 , − r , p + 1 R 0 R 0 δφ , δ v , δ b ∝ ( − r ) λ Radial perturbations: √ √ � � � � � � − 1 , 1 ± 13 , 1 ± 5 2 2 { λ } BSB = , { λ } het = − 1 , ± 2 3 , 1 ± 2 2 2 3 − → two extremality-breaking deformations [two asymptotic fine-tunings?] 24

Geometry: “far-horizon” Away from branes [ r > 0] : assume U ∼ U T = − T e γφ +2 v − 2 q p b Solutions as r → ∞ : φ , v , b ∝ y ( r ) + subleading y ′′ ∼ ˆ T e Ω y + L r 1 2 Ω y ′ 2 + L y ′ ∼ ˆ T e Ω y + L r − M γ 2 − 2( D − 1) � γ 2 − γ 2 � where Ω = D − 2 = D − 2 (IB, Mourad, Sagnotti, 2018) crit 8 D − 2 8 • Orientifolds: φ , v , b ∝ r 2 (due to Ω = 0) • Heterotic: φ , v , b ∝ log( r 0 − r ) 25

Holography of vacuum bubbles (“Bubbleography”) Non-SUSY brane instantons at low energy: vacuum bubbles Spontaneous, irreversible process AdS 3 ( L − ) − → AdS 3 ( L + ) dual “central charge” c − < c + ...holographic description? (Antonelli, IB, Bombini, 2018) • (AdS) vacuum bubbles ← → boundary RG flow • Bubble nucleation ← → ( non-local ) RG trigger • Displaced bubble ← → entanglement pattern of boundary 26

AdS + Conformal singularity AdS − nucleation Bulk → expanding bubble and geodesics Boundary → relevant deformations and RG 27

Our check: bubble entanglement entropy (in 3d) − cosh 2 ρ ± d τ 2 ± + sinh 2 ρ ± d φ 2 � � ds 2 ± = L 2 ± + d ρ 2 ± ± • Thin-wall: geodesic is hyperbolic polygonal length = 2 L − Λ + 2 L − log(cosh ρ − − sinh ρ − cos( θ B − θ A )) + L + cosh − 1 (cosh 2 ρ + − sinh 2 ρ + cos(2 θ B )) + O (Λ − 1 ) • Angle at bubble θ B : no-kink condition gluing condition: L − sinh ρ − = L + sinh ρ + 28