Chern-Simons diffusion rate across different phase transitions

TL;DR

This paper studies how the Chern-Simons diffusion rate behaves across different phase transitions in holographic models, revealing distinct behaviors for first order, second order, and crossover transitions, with implications for QCD phenomena.

Contribution

It provides the first predictions of the Chern-Simons diffusion rate across second order and crossover transitions in strongly coupled non-conformal gauge theories.

Findings

In first order transitions, the rate jumps at the critical temperature.

In second order transitions, the rate's slope becomes infinite.

In crossover transitions, the rate varies smoothly with a rapid change near the pseudo-critical temperature.

Abstract

We investigate how the dimensionless ratio given by the Chern-Simons diffusion rate $\Gamma_{\textrm{CS}}$ divided by the product of the entropy density $s$ and temperature $T$ behaves across different kinds of phase transitions in the class of bottom-up non-conformal Einstein-dilaton holographic models originally proposed by Gubser and Nellore. By tuning the dilaton potential, one is able to holographically mimic a first order, a second order, or a crossover transition. In a first order phase transition, $\Gamma_{\textrm{CS}}/sT$ jumps at the critical temperature (as previously found in the holographic literature), while in a second order phase transition it develops an infinite slope. On the other hand, in a crossover, $\Gamma_{\textrm{CS}}/sT$ behaves smoothly, although displaying a fast variation around the pseudo-critical temperature. In all the cases, $\Gamma_{\textrm{CS}}/sT$ increases with decreasing $T$. The behavior of the Chern-Simons diffusion rate across different phase transitions is expected to play a relevant role for the chiral magnetic effect around the QCD critical end point, which is a second order phase transition point connecting a crossover band to a line of first order phase transition. Our findings in the present work add to the literature the first predictions for the Chern-Simons diffusion rate across second order and crossover transitions in strongly coupled non-conformal, non-Abelian gauge theories.