1. Quantum critical transport, duality, and M-theory hep-th/0701036 Christopher Herzog (Washington) Pavel Kovtun (UCSB) Subir Sachdev (Harvard) Dam Thanh Son (Washington) Talks online at http://sachdev.physics.harvard.edu

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5. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002). Velocity distribution of 87 Rb atoms Superfliud

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7. Outline 1.Boson Hubbard model – conformal field theory (CFT) 2.Hydrodynamics of CFTs 3.Duality 4.SYM 3 with N=8 supersymmetry

8. Outline 1.Boson Hubbard model – conformal field theory (CFT) 2.Hydrodynamics of CFTs 3.Duality 4.SYM 3 with N=8 supersymmetry

9. Boson Hubbard model M.PA. Fisher, P.B. Weichmann, G. Grinstein, and D.S. Fisher Phys. Rev. B 40, 546 (1989).

10. The insulator:

11. Excitations of the insulator:

15. Outline 1.Boson Hubbard model – conformal field theory (CFT) 2.Hydrodynamics of CFTs 3.Duality 4.SYM 3 with N=8 supersymmetry

16. K: a universal number analogous to the level number of the Kac-Moody algebra in 1+1 dimensions M. P. A. Fisher, Phys. Rev. Lett. 65, 923 (1990)

18. Does this matter ?

20. Conformal mapping of plane to cylinder with circumference 1/T

22. Does this matter ?

23. No diffusion of charge, and no hydrodynamics

24. Does this matter ?

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27. K: a universal number analogous to the level number of the Kac-Moody algebra in 1+1 dimensions

30. Superfluid Insulator

31. Superfluid Insulator CFT at T > 0

32. Outline 1.Boson Hubbard model – conformal field theory (CFT) 2.Hydrodynamics of CFTs 3.Duality 4.SYM 3 with N=8 supersymmetry

33. Excitations of the insulator:

34. Approaching the transition from the superfluid Excitations of the superfluid: (A) Spin waves

35. Approaching the transition from the superfluid Excitations of the superfluid: (B) Vortices vortex

36. Approaching the transition from the superfluid Excitations of the superfluid: (B) Vortices vortex E

37. Approaching the transition from the superfluid Excitations of the superfluid: Spin wave and vortices

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40. C. Herzog, P. Kovtun, S. Sachdev, and D.T. Son, hep-th/0701036

41. Outline 1.Boson Hubbard model – conformal field theory (CFT) 2.Hydrodynamics of CFTs 3.Duality 4.SYM 3 with N=8 supersymmetry

46. ImC tt /k 2 CFT at T=0

48. diffusion peak ImC tt /k 2

51. The self-duality of the 4D SO(8) gauge fields leads to C. Herzog, P. Kovtun, S. Sachdev, and D.T. Son, hep-th/0701036

52. The self-duality of the 4D SO(8) gauge fields leads to C. Herzog, P. Kovtun, S. Sachdev, and D.T. Son, hep-th/0701036

53. The self-duality of the 4D SO(8) gauge fields leads to C. Herzog, P. Kovtun, S. Sachdev, and D.T. Son, hep-th/0701036 Holographic self-duality

54. Open questions 1.Does K L K T = constant (i.e. holographic self-duality) hold for SYM 3 SCFT at finite N ? 2.Is there any CFT 3 with an Abelian U(1) current whose conductivity can be determined by self-duality ? (unlikely, because global and topological U(1) currents are interchanged under duality). 3.Is there any CFT 3 solvable by AdS/CFT which is not (holographically) self-dual ? 4.Is there an AdS 4 description of the hydrodynamics of the O(N) Wilson-Fisher CFT 3 ? (can use 1/N expansion to control strongly-coupled gravity theory).