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 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.

5 pages, 1 figure

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• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
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Cited by in corpus (1)

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