# Quantum critical transport, duality, and M theory

## Abstract

We consider charge transport properties of 2+1 dimensional conformal field theories at nonzero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For N=8 supersymmetric, SU(N) Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can be obtained in the large N limit by applying the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to M theory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in 3+1 dimensional anti-de Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in 2+1 dimensional Abelian theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a 'holographic self-duality' in the large N limit, and perhaps more generally.

- Authors:

- Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States)
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030 (United States)
- Department of Physics, Harvard University, Cambridge Massachusetts 02138 (United States)
- Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195-1550 (United States)

- Publication Date:

- OSTI Identifier:
- 21020432

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.75.085020; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; CHARGE TRANSPORT; CONFORMAL INVARIANCE; DE SITTER GROUP; DUALITY; GRAVITATION; HOLOGRAPHY; M-THEORY; QUANTUM FIELD THEORY; SO GROUPS; SU GROUPS; SUPERSYMMETRY; U-1 GROUPS; VORTICES; YANG-MILLS THEORY

### Citation Formats

```
Herzog, Christopher P., Kovtun, Pavel, Sachdev, Subir, and Son, Dam Thanh.
```*Quantum critical transport, duality, and M theory*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.085020.

```
Herzog, Christopher P., Kovtun, Pavel, Sachdev, Subir, & Son, Dam Thanh.
```*Quantum critical transport, duality, and M theory*. United States. doi:10.1103/PHYSREVD.75.085020.

```
Herzog, Christopher P., Kovtun, Pavel, Sachdev, Subir, and Son, Dam Thanh. Sun .
"Quantum critical transport, duality, and M theory". United States.
doi:10.1103/PHYSREVD.75.085020.
```

```
@article{osti_21020432,
```

title = {Quantum critical transport, duality, and M theory},

author = {Herzog, Christopher P. and Kovtun, Pavel and Sachdev, Subir and Son, Dam Thanh},

abstractNote = {We consider charge transport properties of 2+1 dimensional conformal field theories at nonzero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For N=8 supersymmetric, SU(N) Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can be obtained in the large N limit by applying the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to M theory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in 3+1 dimensional anti-de Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in 2+1 dimensional Abelian theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a 'holographic self-duality' in the large N limit, and perhaps more generally.},

doi = {10.1103/PHYSREVD.75.085020},

journal = {Physical Review. D, Particles Fields},

number = 8,

volume = 75,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}