Quantum critical transport, duality, and M-theory hep-th/0701036 Christopher Herzog (Washington) Pavel Kovtun (UCSB) Subir Sachdev (Harvard) Dam Thanh.

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Presentation transcript:

Quantum critical transport, duality, and M-theory hep-th/ Christopher Herzog (Washington) Pavel Kovtun (UCSB) Subir Sachdev (Harvard) Dam Thanh Son (Washington) Talks online at

D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett. 62, 2180 (1989)

Trap for ultracold 87 Rb atoms

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

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

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

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

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

The insulator:

Excitations of the insulator:

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

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)

Does this matter ?

Conformal mapping of plane to cylinder with circumference 1/T

Does this matter ?

No diffusion of charge, and no hydrodynamics

Does this matter ?

K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).

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

Superfluid Insulator

Superfluid Insulator CFT at T > 0

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

Excitations of the insulator:

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

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

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

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

C. Dasgupta and B.I. Halperin, Phys. Rev. Lett. 47, 1556 (1981)

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

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

ImC tt /k 2 CFT at T=0

diffusion peak ImC tt /k 2

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

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

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

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).