Chern-Simons diffusion rate in a holographic Yang-Mills theory

TL;DR

This paper uses holography to compute the Chern-Simons diffusion rate in 4d gauge theories derived from D4-branes, revealing a 6d-like temperature scaling behavior explained through holographic and field theory perspectives.

Contribution

It introduces a novel holographic calculation of the Chern-Simons diffusion rate in D4-brane gauge theories and explains the observed scaling via an extended D4-M5 hydrodynamic map and deconstruction ideas.

Findings

Diffusion rate scales as T^6 at high temperatures with antiperiodic fermions.

Scaling persists at low temperatures with periodic fermions.

Holographic explanation links D4 and M5 hydrodynamics, suggesting a 6d behavior.

Abstract

Using holography, we compute the Chern-Simons diffusion rate of 4d gauge theories constructed by wrapping D4-branes on a circle. In the model with antiperiodic boundary conditions for fermions, we find that it scales like $T^6$ in the high-temperature phase. With periodic fermions, this scaling persists at low temperatures. The scaling is reminiscent of 6d hydrodynamic behavior even at temperatures small compared to compactification scales of the M5-branes from which the D4-branes descend. We offer a holographic explanation of this behavior by adding a new entry to the known map between D4 and M5 hydrodynamics, and suggest a field theory explanation based on "deconstruction" or "fractionization".