410 likes | 580 Views
Quantum critical transport, duality, and M-theory. hep-th/0701036. Christopher Herzog (Washington) Pavel Kovtun (UCSB) Subir Sachdev (Harvard) Dam Thanh Son (Washington). Talk online at http://sachdev.physics.harvard.edu.
E N D
Quantum critical transport, duality, and M-theory hep-th/0701036 Christopher Herzog (Washington) Pavel Kovtun (UCSB) Subir Sachdev (Harvard) Dam Thanh Son (Washington) Talk online at http://sachdev.physics.harvard.edu
D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett.62, 2180 (1989)
Velocity distribution of 87Rb atoms Superfliud M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature415, 39 (2002).
Velocity distribution of 87Rb atoms Insulator M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature415, 39 (2002).
Outline • Boson Hubbard model – conformal field theory (CFT) • Hydrodynamics of CFTs • Duality • SYM3 with N=8 supersymmetry
Outline • Boson Hubbard model – conformal field theory (CFT) • Hydrodynamics of CFTs • Duality • SYM3 with N=8 supersymmetry
Boson Hubbard model M.PA. Fisher, P.B. Weichmann, G. Grinstein, and D.S. Fisher Phys. Rev. B40, 546 (1989).
Outline • Boson Hubbard model – conformal field theory (CFT) • Hydrodynamics of CFTs • Duality • SYM3 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 ? No diffusion of charge, and no hydrodynamics
Does this matter ? K. Damle and S. Sachdev, Phys. Rev. B56, 8714 (1997).
Does this matter ? K. Damle and S. Sachdev, Phys. Rev. B56, 8714 (1997).
K: a universal number analogous to the level number of the Kac-Moody algebra in 1+1 dimensions
K: a universal number analogous to the level number of the Kac-Moody algebra in 1+1 dimensions
Outline • Boson Hubbard model – conformal field theory (CFT) • Hydrodynamics of CFTs • Duality • SYM3 with N=8 supersymmetry
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 E vortex
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. Dasgupta and B.I. Halperin, Phys. Rev. Lett. 47, 1556 (1981)
C. Herzog, P. Kovtun, S. Sachdev, and D.T. Son, hep-th/0701036
Outline • Boson Hubbard model – conformal field theory (CFT) • Hydrodynamics of CFTs • Duality • SYM3 with N=8 supersymmetry
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
The self-duality of the 4D SO(8) gauge fields leads to Holographic self-duality C. Herzog, P. Kovtun, S. Sachdev, and D.T. Son, hep-th/0701036
Open questions • Does KLKT= constant (i.e. holographic self-duality) hold for SYM3 SCFT at finite N ? • Is there any CFT3 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). • Is there any CFT3 solvable by AdS/CFT which is not (holographically) self-dual ? • Is there an AdS4 description of the hydrodynamics of the O(N) Wilson-Fisher CFT3 ? (can use 1/N expansion to control strongly-coupled gravity theory).