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.
- Publication:
-
Physical Review D
- Pub Date:
- April 2007
- DOI:
- 10.1103/PhysRevD.75.085020
- arXiv:
- arXiv:hep-th/0701036
- Bibcode:
- 2007PhRvD..75h5020H
- Keywords:
-
- 73.43.Nq;
- 11.10.Wx;
- 11.25.Yb;
- Quantum phase transitions;
- Finite-temperature field theory;
- M theory;
- High Energy Physics - Theory;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 35 pages, 4 figures