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

In this paper we study the Wiedemann-Franz laws for transport in 2+1 dimensions, and the action of Sl(2, Z) on this transport, for theories with an AdS/CMT dual. We find that Sl(2, Z) restricts the RG-like flow of conductivities and that the Wiedemann-Franz law is (L) over bar=(kappa) over bar/ (T sigma)=cg(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 AdS(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, Z) and can describe vortex conduction and integer quantum Hall effect.

Automated summary

This paper investigates the Wiedemann-Franz laws for transport in 2+1 dimensions and the action of Sl(2, Z) on this transport. It is found that Sl(2, Z) restricts the flow of conductivities and a generalization of effective action can describe vortex conduction and integer quantum Hall effect. The calculated transport coefficients can be matched at large q.