Quantum critical transport, duality, and M-theory

TL;DR

This paper explores charge transport in 2+1D conformal field theories, revealing dualities and deriving exact crossover functions using holography, with implications for understanding quantum criticality and self-duality in strongly coupled systems.

Contribution

It demonstrates a holographic self-duality in 2+1D superconformal Yang-Mills theory via AdS/CFT, connecting particle-vortex duality and electromagnetic duality in gravity.

Findings

Particle-vortex duality constrains hydrodynamic-to-collisionless crossover functions.

Exact crossover functions are obtained for SO(8) R-currents in large N limit.

Holographic self-duality links 2+1D CFTs to 3+1D gravity theories.

Abstract

We consider charge transport properties of 2+1 dimensional conformal field theories at non-zero 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 the 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 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.