Emergent IR D ual 2d CFTs in Charged AdS 5 Black H oles

1. Emergent IR Dual 2d CFTs in Charged AdS5 Black Holes Maria Johnstone(University of Edinburgh) • Korea Institute for Advanced Study (KIAS) • 20th February 2012

2. Emergent IR Dual 2d CFTs in Charged AdS5 Black Holes arXiv:1112.4664v1 Jan de Boer, M. M. Sheikh-Jabbari, Joan Simon

3. Plan • Introduce the EVH/CFT proposal • Take the near horizon limit of Near BPS near EVH R-Charged black holes • Discuss the near horizon AdS3 geometry and emergent CFT2 • Connection between CFT4 dual to AdS5 and the CFT2 dual to AdS3 • Relationship between the EVH/CFT proposal and the Extremal Black Hole/CFT Correspondence (finite horizon)

4. not well-understood ? seems to contain no dynamics

5. ? • not well-understood • seems to contain no dynamics

6. AdS5xS5 CFT4=SU(N) SYM Near Horizon IR Limit Near Horizon Geometry Low energy Limit

7. AdS5xS5 CFT4=SU(N) SYM Near Horizon IR Limit Near Horizon Geometry Low energy Limit central charge of the CFT.

8. AdS5xS5 CFT4=SU(N) SYM Near Horizon IR Limit (No dynamics) Near Horizon Geometry Low energy Limit central charge of the CFT.

9. AdS5xS5 CFT4=SU(N) SYM Near Horizon IR Limit (No dynamics) Near Horizon Geometry Low energy Limit central charge of the CFT. • Probing the system at sufficiently low energies above the black hole, but below the gap, one expects no non-trivial dynamics • Near horizon limit kills all the non-trivial dynamics in the IR regime unless together with the N.H. limit we also decrease the mass gap by taking • This will generically take the entropy to infinity unless we take temperature to zero too…

10. This generically takes the entropy to infinity unless we take temperature to zero too: For any thermodynamic system, and in particular a black hole, the entropy admits a low temperature expansion: Extremal Black Hole: T=0, S blows up for large N in the IR limit, large N , Small T This is the property of a CFT2, Cardyformula: dual IR k+1 dimensional CFT,

11. Extremal Vanishing Horizon (EVH) Black Holes Entropy remains finite in the EVH limit, only if we scale Newton’s constant in the same rate as the horizon area. So taking the large N limit sends both the 5d Newtons constant and the mass gap of the “UV CFT” to zero. In the N.H. limit we obtain an AdS3 throat

12. Extremal Vanishing Horizon (EVH) Black Holes • N.H. limit of EVH black holes contains an AdS3 throat. • We will study the near horizon geometry of AdS5 static near EVH black holes in certain large N limit, and the IR emergent 2d CFT.

13. Extremal Vanishing Horizon (EVH) Black Holes • For asymptotic AdS5 EVH black holes we have a UV CFT4 and an IR 2d CFT. • We would like to relate quantum numbers of UV CFT and the 2d IR CFT’s.

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21. R Charged AdS5 Black Holes 10d Metric: RR 4-form potential:

22. R Charged AdS5 Black Holes 10d Metric: 5d Black Hole Metric

23. R Charged AdS5 Black Holes 10d Metric:

24. R Charged AdS5 Black Holes Mass: R Charges:

25. Interpretation as Giant Gravitons • Distribution of giant gravitons • One type of giant for each charge: one corresponding to each 3-cycle in the transverse 5 sphere • Number of giants in each stack : • Pairs of giants intersect on circles It has been suggested in the literature that an AdS5 black hole with two R charges should allow a dual 2d CFT description defined on the circle where giants intersect, and that the central charge of this CFT is proportional to the total number of these intersections

26. Extremal Vanishing Horizon Condition Entropy: Temperature: Extremal Vanishing Horizon Condition:

27. There are two physically distinct EVH cases: temperature scales to zero. • Near-extremalnon-BPS: • Near-extremalnear-BPS: -a dilute gas of giant gravitons in which the black hole temperature remains finite -total number of giant graviton intersections:

28. Near Horizon Limit Near BPS: Near Extremal: Near Horizon Limit:

29. Near Horizon Geometry

30. Near Horizon Geometry

31. Near Horizon Geometry

32. Near Horizon Geometry

33. Near Horizon Geometry BTZ geometry:

34. Near Horizon AdS3 BTZ geometry:

35. Near Horizon AdS3 Reducing 10d IIB SUGRA over S3 ×M4: 3d Newton constant: 5d entropy: 3d entropy:

36. Near Horizon AdS3 Focus on Strip of S5: Each strip lies at Entropy density: Sum over entropies:

37. Scaling of N Overall epsilon scaling: Decoupling limit of the AdS/CFT correspondence: send the string length to zero: Keeping the AdS5 radius constant then requires that we scale N to infinity as

38. Scaling of N Although the bulk entropy vanishes, its entropy density is finite

39. The CFT4 • Taking the near-horizon limit on the gravity backgrounds corresponds to taking a low energy limit in the N = 4, d = 4 U(N) SYM theory. • In the near-BPS limit it corresponds to focusing on specific sector in the N = 4 SYM which we identify.

40. The CFT4 Scaling Dimension: R Charge: Deviation from BPS: finite

41. CFT4vs CFT2

42. CFT4vs CFT2

43. CFT4vs CFT2

44. CFT4vs CFT2 CFT4 CFT2

45. CFT4vs CFT2 • The vacuum of the 2d CFT: = 1/4 BPS black hole

46. Extremal Black Hole/CFT Correspondence “Low energy excitations around any finite horizon, extremal black hole is described by a chiral 2d CFT with a given central charge c , read from Asymptotic Symmetry Group (ASG) analysis in the N.H. geometry of the black hole, and at Frolov-Thorone temperature T”.

47. Extremal Black Hole/CFT Correspondence “Low energy excitations around any finite horizon, extremal black hole is described by a chiral 2d CFT with a given central charge c , read from Asymptotic Symmetry Group (ASG) analysis in the N.H. geometry of the black hole, and at Frolov-Thorone temperature T”.

48. Extremal Black Hole/CFT Correspondence

49. Extremal Black Hole/CFT Correspondence Central Charge:

50. Extremal Black Hole/CFT Correspondence For extremal R-charged AdS5 we have three U(1) isometries, three charges, associated with three independent rotations in S5 There exist three inequivalent chiral CFTs reproducing the black hole entropy. central charges are fixed by the “Cardy formula”.