Wiedemann-Franz laws and $Sl(2,\mathbb{Z})$ duality in AdS/CMT holographic duals and one-dimensional effective actions for them

Abstract

In this paper we study the Wiedemann-Franz laws for transport in 2+1 dimensions, and the action of $Sl(2,\mathbb{Z})$ on this transport, for theories with an AdS/CMT dual. We find that $Sl(2,\mathbb{Z})$ restricts the RG-like flow of conductivities and that the Wiedemann-Franz law is $\bar{L}=\bar{\kappa }/(T\sigma )=c{g}_4^2\pi /3$, from the weakly coupled} gravity dual. In a self-dual theory this value is also the value of $L=\kappa /(T\sigma )$ in the weakly coupled field theory description. Using the formalism of a 0+1 dimensional effective action for both generalized $SY{K}_q$ models and the $Ad{S}_4$ gravity dual, we calculate the transport coefficients and show how they can be matched at large $q$. We construct a generalization of this effective action that is invariant under $Sl(2,\mathbb{Z})$ and can describe vortex conduction and integer quantum Hall effect.

51 pages, 2 figures; references added, clarifications for comparison with reference, and about our results, added

References in corpus (10)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Anderson Transitions
• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Quantum critical transport, duality, and M-theory
• Hall conductivity from dyonic black holes
• Universal low temperature theory of charged black holes with AdS${}_2$ horizons
• Magneto-thermal transport implies an incoherent Hall conductivity
• Particle-vortex and Maxwell duality in the $Ad{S}_4\times {\mathbb{CP}}^3$/ABJM correspondence
• Conductivities from attractors

Cited by in corpus (2)

• On the hydrodynamics of (2 + 1)-dimensional strongly coupled relativistic theories in an external magnetic field
• Thermoelectric properties and Wiedemann-Franz like relations in mixed-dimensional QEDs from particle-vortex dualities