Probing Black Hole Microstates Stefano Giusto October 18-19 2019 - PowerPoint PPT Presentation

Probing Black Hole Microstates Stefano Giusto October 18-19 2019 PRIN Kickoff Meeting - SNS

Overview

The Hawking paradox Classical horizon ⇒ → % $ (i) AB are maximally entangled ⇒ , → • (ii) A cannot be entangled with C ⇒ information loss ! Possible way outs Typical black hole microstates have a smooth horizon but there are non-local effects linking A to C ⇒ (ii) does not hold (ER=EPR, Papadodimas-Raju, . . . ) Effective field theory fails at distances of the order of the black hole horizon and a typical microstate does not have a smooth horizon ⇒ (i) does not hold (Fuzzballs, firewalls, . . . ) 1

A holographic perspective In some situations, a black hole is dual to an ensemble in a 2D CFT decoupling holography → AdS 3 → 2D CFT Black hole − − − − − − − − ← − − − − − − − A b.h. microstate is dual to a “heavy” operator O H (∆ H ∼ c ≫ 1) What is the description of O H when g 2 s c ≫ 1 ? g 2 g 2 s c ≫ 1 s c ≪ 1 (EFT) R H ← → l p ds 2 O H H 2

A holographic perspective In some situations, a black hole is dual to an ensemble in a 2D CFT decoupling holography → AdS 3 → 2D CFT Black hole − − − − − − − − ← − − − − − − − A b.h. microstate is dual to a “heavy” operator O H (∆ H ∼ c ≫ 1) What is the description of O H when g 2 s c ≫ 1 ? g 2 s c ≪ 1 g 2 s c ≫ 1 (Fuzzball) ← → R H ds 2 O H H 2

The fuzzball program • Smooth geometries dual to susy b.h. microstates are known • We have some (but limited) results for non-susy b.h. • There are non-trivial checks of the duality between ds 2 H and O H • The known geometries capture a parametrically small fraction of the entropy of b.h. with a classically macroscopic horizon 3

The fuzzball program • Smooth geometries dual to susy b.h. microstates are known • We have some (but limited) results for non-susy b.h. • There are non-trivial checks of the duality between ds 2 H and O H • The known geometries capture a parametrically small fraction of the entropy of b.h. with a classically macroscopic horizon Can typical b.h. microstates be described in supergravity? 3

The fuzzball program • Smooth geometries dual to susy b.h. microstates are known • We have some (but limited) results for non-susy b.h. • There are non-trivial checks of the duality between ds 2 H and O H • The known geometries capture a parametrically small fraction of the entropy of b.h. with a classically macroscopic horizon Can typical b.h. microstates be described in supergravity? • Even if the answer is no, known microstates geometries encode non-trivial information on the CFT at strong coupling 3

Probing the microstates • Microstates can be probed by “light” operators O L (∆ L ∼ O ( c 0 )) • 4-point correlators � ¯ O H ( ∞ ) O H (0) O L ( z ) ¯ → � O L ( z ) ¯ O L (1) � ← O L (1) � ds 2 H • They are non-protected and have informations on non-susy operators • They diagnose information loss: they cannot decay at large t • Correlators with O H cannot be computed with Witten diagrams • Witten diagrams in AdS 3 are subtle: no holographic correlator in a 2D CFT had been computed before • In a certain limit: � ¯ O H O H O L ¯ O L � → � ¯ O L O L O L ¯ O L � 4

Probing the microstates • Microstates can be probed by “light” operators O L (∆ L ∼ O ( c 0 )) • 4-point correlators � ¯ O H ( ∞ ) O H (0) O L ( z ) ¯ → � O L ( z ) ¯ O L (1) � ← O L (1) � ds 2 H • They are non-protected and have informations on non-susy operators • They diagnose information loss: they cannot decay at large t • Correlators with O H cannot be computed with Witten diagrams • Witten diagrams in AdS 3 are subtle: no holographic correlator in a 2D CFT had been computed before • In a certain limit: � ¯ O H O H O L ¯ O L � → � ¯ O L O L O L ¯ O L � Microstate geometries provide an alternative method to compute holographic correlators 4

Plan of the talk The D1-D5-P black hole and the dual CFT Construction of the microstate geometries Holographic correlators and consistency with unitarity Outlook and open problems 5

The D-brane system

The D1-D5-P black hole (Strominger, Vafa) The extremal 3-charge black hole in type IIB on R 4 , 1 × S 1 × T 4 → AdS 3 × S 3 × T 4 ← decoupling D 1 5 D 5 12345 P 5 → 2D CFT − − − − − − − − with vol ( T 4 ) ∼ ℓ 4 s and R ( S 1 ) ≫ ℓ s The 2D CFT is the (4 , 4) D1D5 CFT with c = 6 n 1 n 5 ≡ 6 N ≫ 1 The CFT has a 20-dim moduli space: free orbifold point ← → R AdS ≪ ℓ s strong coupling point ← → R AdS ≫ ℓ s 6

The D1-D5 CFT Symmetries: → S 3 rotations (4,4) SUSY with SU (2) L × SU (2) R R-symmetry ← The symmetry algebra is generated by: L n , J n , G n +1 / 2 The orbifold point: sigma-model on ( T 4 ) N / S N The elementary fields are 4 bosons, 4 fermions and twist fields Chiral primary operators: j ) with h = j , ¯ h = ¯ O ( j , ¯ j (and their descendants with respect to the symmetry algebra) are protected: conformal dimensions and 3-point functions do not depend on the moduli 7

Microstate geometries

The graviton gas If O k is a (anti)CPO of dimension k one can consider its descendants with respect to the global symmetry algebrra 2 ) q O k O k , m , n , q ≡ ( J + 0 ) m ( L − 1 ) n ( G +1 2 G +2 − 1 − 1 “Semi-classical” states are coherent states ( B 1 O k 1 , m 1 , n 1 , q 1 ) p 1 ( B 2 O k 2 , m 2 , n 2 , q 2 ) p 2 . . . | 0 � � | B 1 , B 2 , . . . � ≡ p 1 , p 2 ,... When B 2 i ∼ N ≫ 1 the p i -sum is peaked for p i ≈ B 2 i / k 8

The graviton gas If O k is a (anti)CPO of dimension k one can consider its descendants with respect to the global symmetry algebrra 2 ) q O k O k , m , n , q ≡ ( J + 0 ) m ( L − 1 ) n ( G +1 2 G +2 − 1 − 1 “Semi-classical” states are coherent states ( B 1 O k 1 , m 1 , n 1 , q 1 ) p 1 ( B 2 O k 2 , m 2 , n 2 , q 2 ) p 2 . . . | 0 � � | B 1 , B 2 , . . . � ≡ p 1 , p 2 ,... When B 2 i ∼ N ≫ 1 the p i -sum is peaked for p i ≈ B 2 i / k What is the gravitational description of | B 1 , B 2 , . . . � ? 8

Superstrata: construction → AdS 3 × S 3 | 0 � ← Holography associates to O k a sugra field φ k : O k ← → φ k At linear order in B i | B 1 , . . . � is a perturbation of the vacuum → AdS 3 × S 3 + B i φ k i , m i , n i , q i | 0 � + B i O k i , m i , n i , q i | 0 � ← where φ k i , m i , n i , q i solves the linearised sugra eqs. around AdS 3 × S 3 ρ n sin k − m θ cos m θ e i [( k − m ) φ − m ψ +( k + n ) τ + n σ ] φ k , m , n , 0 = ( ρ 2 + 1) n + k 2 One can extend the linearised solution to an exact solution of the sugra eqs. valid for B 2 i ∼ N The non-linear extension is non-unique: ambiguities are fixed by imposing regularity 9

Superstrata: result The non-linear solutions are smooth and horizonless The solutions are asymptotically AdS 3 × S 3 but in the interior AdS 3 and S 3 are non-trivially mixed The solutions can be glued back to flat space → R 4 , 1 × S 1 (after spectral flow to the R sector) There is a continuous family of solutions, parametrised by B i , for fixed values of the global D1, D5, P charges R 4 , 1 × S 1 AdS 3 × S 3 ← − r ∼ R Hor no horizon! 10

Holographic probes

HHL correlators (Kanitscheider, Skenderis, Taylor; SG, Moscato, Rawash, Russo, Turton) Consider � O L � H ≡ � ¯ O H ( ∞ ) O H (0) O L (1) � with holography p 1 ,... ( B 1 O k 1 , m 1 , n 1 , q 1 ) p 1 . . . → ds 2 O H = � ← − − − − − − − H holography → φ k O L = O k ← − − − − − − − � ¯ O H O H O L � do not depend on the CFT moduli ⇒ One can extract � O k � H from the geometry ds 2 H ρ →∞ ρ − k � O k � H φ k − → and compare with the value computed in the orbifold CFT What we learn: Microstate geometries must have non-trivial multiple moments Non-trivial checks of the sugra construction, including the non-linear completion 11

HHLL correlators How to compute holographically z ) ≡ � ¯ z ) ¯ C H ( z , ¯ O H ( ∞ ) O H (0) O L ( z , ¯ O L (1) � O L ( z , ¯ z ) ≡ O k ( z , ¯ z ) ← → φ k ( ρ ; z , ¯ z ) Solve the linearised e.o.m. for φ k in the background ds 2 H ← → O H Pick the non-normalisable solution such that at the boundary ( ρ → ∞ ) vev of O L ( z , ¯ z ) ր → δ ( z − 1) ρ k − 2 + b ( z , ¯ ρ →∞ z ) ρ − k φ k ( ρ ; z , ¯ z ) − ց source for ¯ O L (1) in the interior ( ρ → 0) φ ( ρ ; z , ¯ z ) is regular The correlator is given by z ) ¯ C H ( z , ¯ z ) = � O H | O L ( z , ¯ O L (1) | O H � = b ( z , ¯ z ) 12

A simple example (Bombini, Galliani, SG, Moscato, Russo) We take � ( B O 1 ) p O H = , O L = O 1 p O H is a chiral primary ⇒ P = 0 The ensemble of chiral primaries corresponds to a “small black hole” (massless limit of BTZ) ds 2 = d ρ 2 ρ 2 + ρ 2 ( − d τ 2 + d σ 2 ) + d Ω 2 3 R 2 AdS The geometry ds 2 H dual to O H approximates the small black hole geometry in the limit B 2 → N Computing C H for heavy states with P � = 0 and finite B is harder, but see also Bena, Heidmann, Monten, Warner 13