On the Universality of the Chern-Simons Diffusion Rate

TL;DR

This paper proves the universality of the Chern-Simons diffusion rate in a broad class of holographic gauge theories, showing it depends only on temperature, entropy, and coupling, with implications for the chiral magnetic effect.

Contribution

It extends the proof of the universal Chern-Simons diffusion rate to various holographic models, including those with magnetic fields and anisotropy, and discusses subtleties in defining the rate with anomalies.

Findings

The diffusion rate is universal and depends only on thermodynamic quantities.

The rate's usual definition vanishes in the presence of anomalies, requiring alternative approaches.

A non-trivial relaxation time can be obtained from quasi-normal mode analysis.

Abstract

We prove the universality of the Chern-Simons diffusion rate - a crucial observable for the chiral magnetic effect - in a large class of planar strongly correlated gauge theories with dual string description. When the effects of anomalies are suppressed, the diffusion rate is simply given in terms of temperature, entropy density and gauge coupling, with a universal numerical coefficient. We show that this result holds, in fact, for all the top-down holographic models where the calculation has been performed in the past, even in presence of magnetic fields and anisotropy. We also extend the check to further well known models for which the same computation was lacking. Finally we point out some subtleties related to the definition of the Chern-Simons diffusion rate in the presence of anomalies. In this case, the usual definition of the rate - a late time limit of the imaginary part of the retarded correlator of the topological charge density - would give an exactly vanishing result, due to its relation with a non-conserved charge correlator. We confirm this observation by explicit holographic computations on generic isotropic black hole backgrounds. Nevertheless, a non-trivial Chern-Simons relaxation time can in principle be extracted from a quasi-normal mode calculation.