  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".
