Chern-Simons diffusion rate across different phase transitions

We investigate how the dimensionless ratio given by the Chern-Simons diffusion rate ΓCS 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 nonconformal 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, ΓCS/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, ΓCS/sT behaves smoothly, although displaying a fast variation around the pseudo-critical temperature. In all the cases, ΓCS/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 nonconformal, non-Abelian gauge theories.