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Quantum critical transport, duality, and M-theory

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.

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Quantum critical transport, duality, and M-theory

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  1. 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

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

  3. Trap for ultracold 87Rb atoms

  4. Velocity distribution of 87Rb atoms Superfliud M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature415, 39 (2002).

  5. Velocity distribution of 87Rb atoms Insulator M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature415, 39 (2002).

  6. Outline • Boson Hubbard model – conformal field theory (CFT) • Hydrodynamics of CFTs • Duality • SYM3 with N=8 supersymmetry

  7. Outline • Boson Hubbard model – conformal field theory (CFT) • Hydrodynamics of CFTs • Duality • SYM3 with N=8 supersymmetry

  8. Boson Hubbard model M.PA. Fisher, P.B. Weichmann, G. Grinstein, and D.S. Fisher Phys. Rev. B40, 546 (1989).

  9. The insulator:

  10. Excitations of the insulator:

  11. Excitations of the insulator:

  12. Outline • Boson Hubbard model – conformal field theory (CFT) • Hydrodynamics of CFTs • Duality • SYM3 with N=8 supersymmetry

  13. 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)

  14. Does this matter ?

  15. Does this matter ? No diffusion of charge, and no hydrodynamics

  16. Does this matter ? K. Damle and S. Sachdev, Phys. Rev. B56, 8714 (1997).

  17. Does this matter ? K. Damle and S. Sachdev, Phys. Rev. B56, 8714 (1997).

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

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

  20. Outline • Boson Hubbard model – conformal field theory (CFT) • Hydrodynamics of CFTs • Duality • SYM3 with N=8 supersymmetry

  21. Excitations of the insulator:

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

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

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

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

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

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

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

  29. Outline • Boson Hubbard model – conformal field theory (CFT) • Hydrodynamics of CFTs • Duality • SYM3 with N=8 supersymmetry

  30. 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

  31. 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

  32. 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).

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