Quantum critical transport, duality, and Mtheory

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
2
D. B. Haviland, Y. Liu, and A. M. Goldman, Phys.
Rev. Lett. 62, 2180 (1989)
3
Trap for ultracold 87Rb atoms
4
(No Transcript)
5
Velocity distribution of 87Rb atoms
Superfliud
M. Greiner, O. Mandel, T. Esslinger, T. W.
Hänsch, and I. Bloch, Nature 415, 39 (2002).
6
Velocity distribution of 87Rb atoms
Insulator
M. Greiner, O. Mandel, T. Esslinger, T. W.
Hänsch, and I. Bloch, Nature 415, 39 (2002).
7
Outline

• Boson Hubbard model conformal field theory
  (CFT)
• Hydrodynamics of CFTs
• Duality
• SYM3 with N8 supersymmetry

8
Outline

• Boson Hubbard model conformal field theory
  (CFT)
• Hydrodynamics of CFTs
• Duality
• SYM3 with N8 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
12
Excitations of the insulator
13
(No Transcript)
14
(No Transcript)
15
Outline

• Boson Hubbard model conformal field theory
  (CFT)
• Hydrodynamics of CFTs
• Duality
• SYM3 with N8 supersymmetry

16
K a universal number analogous to the level
number of the Kac-Moody algebra in 11 dimensions
M. P. A. Fisher, Phys. Rev. Lett. 65, 923 (1990)
17
(No Transcript)
18
Does this matter ?
19
(No Transcript)
20
Conformal mapping of plane to cylinder with
circumference 1/T
21
Conformal mapping of plane to cylinder with
circumference 1/T
22
Does this matter ?
23
Does this matter ?
No diffusion of charge, and no hydrodynamics
24
Does this matter ?
25
Does this matter ?
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714
(1997).
26
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714
(1997).
27
K a universal number analogous to the level
number of the Kac-Moody algebra in 11 dimensions
28
K a universal number analogous to the level
number of the Kac-Moody algebra in 11 dimensions
29
(No Transcript)
30
Insulator
Superfluid
31
CFT at T gt 0
Insulator
Superfluid
32
Outline

• Boson Hubbard model conformal field theory
  (CFT)
• Hydrodynamics of CFTs
• Duality
• SYM3 with N8 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
E
vortex
37
Approaching the transition from the superfluid
Excitations of the superfluid Spin wave and
vortices
38
C. Dasgupta and B.I. Halperin, Phys. Rev. Lett.
47, 1556 (1981)
39
C. Dasgupta and B.I. Halperin, Phys. Rev. Lett.
47, 1556 (1981)
40
C. Herzog, P. Kovtun, S. Sachdev, and D.T. Son,
hep-th/0701036
41
Outline

• Boson Hubbard model conformal field theory
  (CFT)
• Hydrodynamics of CFTs
• Duality
• SYM3 with N8 supersymmetry

42
(No Transcript)
43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
CFT at T0
ImCtt/k2
47
(No Transcript)
48
diffusion peak
ImCtt/k2
49
(No Transcript)
50
(No Transcript)
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
Holographic self-duality
C. Herzog, P. Kovtun, S. Sachdev, and D.T. Son,
hep-th/0701036
54
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).