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

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Trap for ultracold 87 Rb atoms

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

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

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

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

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The insulator:

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Excitations of the insulator:

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

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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)

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Does this matter ?

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Conformal mapping of plane to cylinder with circumference 1/T

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Does this matter ?

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No diffusion of charge, and no hydrodynamics

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Does this matter ?

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

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

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Superfluid Insulator

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Superfluid Insulator CFT at T > 0

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

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Excitations of the insulator:

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

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

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

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

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

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

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

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ImC tt /k 2 CFT at T=0

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diffusion peak ImC tt /k 2

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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

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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

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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

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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).

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