# S-duality, entropy function and transport in $AdS_4/CMT_3$

## TL;DR

This paper explores how S-duality influences transport properties in 2+1D holographic models with Abelian gauge fields and scalars, using entropy function and Stokes equation formalisms to analyze extremal and lattice cases.

## Contribution

It introduces a comprehensive analysis of S-duality effects on transport coefficients in holographic condensed matter models, employing entropy function and holographic Stokes equations.

## Key findings

- S-duality relates electric and heat conductivities in the models.
- Entropy function formalism effectively computes extremal black hole properties.
- Holographic Stokes equations describe transport in lattice systems.

## Abstract

In this paper we consider Abelian vector plus scalar holographic gravity models for 2+1 dimensional condensed matter transport, and the effect of S-duality on them. We find the transport coefficients from the electric and heat currents via usual membrane paradigm-type calculations, and the effect of S-duality on them. We study the same system also by using the entropy function formalism in the extremal case, and the formalism of holographic Stokes equations, in the case of one-dimensional lattices. We study a few generalizations that appear when considering a supergravity-inspired model, and apply the entropy function method for them.