1 / 22

Anti de Sitter Black Holes

Anti de Sitter Black Holes. Harvey Reall University of Nottingham. Motivation. Black hole entropy calculations all rely on 2d CFT Can we use AdS/CFT to calculate entropy of D>3 AdS black holes? D=4: probably not, CFT not understood D=5: CFT is N =4 SYM…

samanthaw
Download Presentation

Anti de Sitter Black Holes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Anti de Sitter Black Holes Harvey Reall University of Nottingham

  2. Motivation • Black hole entropy calculations all rely on 2d CFT • Can we use AdS/CFT to calculate entropy of D>3 AdS black holes? • D=4: probably not, CFT not understood • D=5: CFT is N=4 SYM… • Need supersymmetric AdS5 black holes to evade strong coupling problem

  3. Plan • SUSY asymptotically flat black holes • SUSY AdS black holes in D=3,4 • SUSY AdS black holes in D=5 • CFT interpretation • Collaborators: J. Gutowski, R. Roiban, H. Kunduri, J. Lucietti

  4. SUSY 5D black holesHSR 02, Gutowski 04 • 5D ungauged N=1 sugra + abelian vectors • Introduce coordinates adapted to horizon • Take near-horizon limit • Impose supersymmetry: eqs on spatial cross-section of horizon • Can determine general solution for compact horizon

  5. SUSY 5D black holesHSR 02, Gutowski 04 • All possible near-horizon geometries: • Which arise from asymp flat black holes? • Near-horizon BMPV from BMPV! • AdS3xS2 from BPS black rings Elvang et al 04 • Flat T3 horizon unlikely Galloway 06

  6. SUSY AdS Black Holes • BPS limit of Reissner-Nordstrom-AdS is nakedly singular • D=3: BTZ is SUSY black hole iff M=|J|>0 • D=4: Kerr-Newman-AdS (M,J,Q,P) saturates BPS bound if M=M(Q), J=J(Q), P=0 Kostalecky & Perry 95, Caldarelli & Klemm 98 • SUSY AdS black holes must rotate

  7. 5D SUSY AdS black holesGutowski& HSR 04 • Reduce IIB SUGRA on S5 to N=1 D=5 U(1)3 gauged SUGRA Cvetic et al 99 • Canonical form for SUSY solutions involves specifying 4d Kähler “base space” Gauntlett & Gutowski 03, Gutowski & HSR 04 • Choice of base space not obvious e.g. get AdS5 from Bergman manifold SU(2,1)/U(2)

  8. 5D SUSY AdS black holesGutowski& HSR 04 • Seek SUSY black holes systematically by examining near-horizon geometry • In near-horizon limit, conditions for SUSY are equations on 3-manifold • General solution not known • Particular homogeneous S3 solution can be found (cf near-horizon BMPV)

  9. 5D SUSY AdS black holesGutowski& HSR 04 • Near-horizon solution motivates cohomogeneity-1 Ansatz for full solution • First examples of SUSY AdS5 black holes! • Base space singular, cohomogeneity-1, asymptotically Bergman space • 1/16 BPS

  10. Unequal Angular MomentaChong, Cvetic, Lü & Pope 05 • Guessed non-BPS charged rotating black hole solution of minimal gauged sugra (Einstein-Maxwell) • Cohomogeneity-2, 4 parameters (M,J1,J2,Q) • BPS limit: 2 parameter solution with J1≠J2

  11. General solutionKunduri, Lucietti & HSR 06 • Determine base space of BPS solution of minimal gauged sugra: singular, cohomogeneity-2, asymptotically Bergman • Plug into BPS eqs of U(1)3 gauged sugra, solve… • BPS solution parametrized by J1, J2, Q1, Q2, Q3 with one constraint • Expect non-BPS generalization with independent M,J,Q (2 more parameters)

  12. CFT description • BPS AdS5 black hole microstates are 1/16 BPS states of N=4 large N SYM on RxS3 (equivalently BPS local operators on R4) • States classified by SO(4)xSO(6) quantum numbers J,Q • Black hole quantum numbers O(N2) • Black hole entropy O(N2) • Entropy calculation: count all 1/16 BPS states with same quantum numbers as black hole

  13. A Puzzle • 1/16 BPS states have independent J,Q • Why do BPS black holes have a constraint relating J,Q? • Is there a more general family of SUSY black holes with independent J,Q? • But corresponding non-SUSY solution would need more than just conserved charges to specify it • BPS AdS black rings?

  14. BPS AdS black rings?Kunduri, Lucietti & HSR 06 • Most general BPS near-horizon geometry in 5D gauged sugra not known • Assume existence of 2 rotational symmetries (true for all known 5d black holes): problem reduces to ODEs. 2 interesting solutions. • One solution is near-horizon geometry of known S3 black holes • Another solution is a warped product AdS3xS2 with horizon topology S1xS2…

  15. BPS AdS black rings?Kunduri, Lucietti & HSR 06 • …but with a conical singularity on S2 • Can’t eliminate singularity (without turning off cosmological constant) • BPS AdS black rings with 2 rotational symmetries do not exist • Oxidize to 10d: warped product AdS3xM7 with M7=S2xS5 (singular)

  16. New 10d black holes? • Solution is locally isometric to AdS3xM7 solution of Gauntlett et al 06 • They showed that solution can be made globally regular by choosing topology of M7 appropriately (not S2xS5) • Resulting solution cannot be reduced to 5d • Could this be near-horizon geometry of an asymptotically AdS5xS5 black hole?

  17. Resolutions of the puzzle? • Are there BPS 10d black hole solutions that can’t be reduced to 5d? • Are there BPS 5d black holes without 2 rotational symmetries? • Non-abelian BPS black holes? • Maybe we know most general black hole. 1/16 BPS states have 5 charges but perhaps only 4 charge subset has O(N2) entropy Berkooz et al 06

  18. CFT entropy calculation? • Need to count 1/16 BPS states of N=4 SU(N) SYM on RxS3 (or local operators on R4) with same quantum numbers O(N2) as black hole • Black hole entropy O(N2) • States typically descendents but need large entropy O(N2) in primaries

  19. No 1/8 BPS black holesRoiban & HSR 04, Berenstein 05 • 1/8 BPS primaries built from N=1 superfields Xi,W • Commutators give descendents, so Xi, W can be treated as commuting • Diagonalize: O(N) degrees of freedom so entropy of primaries of length O(N2) is O(N log N), too small for bulk horizon

  20. Weakly coupled CFTRoiban & HSR 04, Kinney, Maldacena, Minwalla & Raju 05 • Goal: at weak coupling, count operators in short 1/16 BPS multiplets that can’t become long at strong coupling • Too hard! Count everything instead… • Find correct scaling of entropy with charge for large charge

  21. Superconformal IndexKinney, Maldacena, Minwalla & Raju 05 • Vanishing contribution from states in short multiplets that can combine into long ones • Independent of N at large N: doesn’t “see” black holes • Cancellation between bosonic and fermionic BPS states dual to black hole

  22. Summary • There is a 4-parameter family of 1/16 BPS black holes in AdS5 • Why only 4 parameters? • How do we calculate their entropy using N=4 SYM?

More Related