Topological transport from a black hole

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 CFT2+1, while the direct electric conductivity vanishes; the thermoelectric conductivity is non-zero at vanishing temperature, while the O(T) behavior, controlled by the Mott relation, is subleading. Provided that the entropy of the black hole, and the dual system, is non-vanishing at T=0, the observations indicate that the dyonic black hole describes a ħ→0 limit of a highly degenerate topological state, in which the black hole charge measures the density of excited non-abelian quasiparticles. The holographic description gives further evidence that non-abelian nature of quasiparticles can be determined by the low temperature behavior of the thermoelectric transport.