# Topological transport from a black hole

## TL;DR

This paper explores the topological transport properties of a 2+1-dimensional system dual to a dyonic black hole, revealing features like the Wiedemann-Franz law and non-zero thermoelectric conductivity at zero temperature.

## Contribution

It demonstrates that a dyonic black hole models a highly degenerate topological state with classical transport features, connecting black hole physics to condensed matter phenomena.

## Key findings

- Transverse conductivities satisfy Wiedemann-Franz law.
- Direct heat conductivity scales with the dual CFT's central charge.
- Electric conductivity vanishes at zero temperature.

## Abstract

In this paper the low temperature zero-frequency transport in a 2+1-dimensional theory dual to a dyonic black hole is discussed. It is shown that transport exhibits topological features: the transverse electric and heat conductivities satisfy the Wiedemann-Franz law of free electrons; the direct heat conductivity is measured in units of the central charge of the dual CFT, while the direct electric conductivity vanishes; the thermoelectric conductivity is non-zero at vanishing temperature, while the linear in temperature behaviour, controlled by the Mott relation, is subleading. Provided that the entropy of the black hole, and the dual system, is non-vanishing at zero temperature, the observations indicate that the dyonic black hole describes a "classical" limit of a highly degenerate topological state, in which the black hole charge measures the density of excited non-abelian quasiparticles.