Non-Abelian chiral instabilities at high temperature on the lattice

TL;DR

This study uses lattice simulations to explore how chiral instabilities in non-Abelian gauge theories at high temperature influence topological charge dynamics and chiral imbalance, relevant for early universe and heavy-ion collision physics.

Contribution

It provides the first lattice-based analysis of chiral instabilities using an anomalous Langevin effective theory at high temperature.

Findings

Rapid energy increase in soft gauge fields at early times.

Diffusion rate of topological charge depends on initial chiral density.

Chiral imbalance decreases monotonously over time.

Abstract

We report on an exploratory lattice study on the phenomenon of chiral instabilities in non-Abelian gauge theories at high temperature. It is based on a recently constructed anomalous Langevin-type effective theory of classical soft gauge fields in the presence of a chiral number density $n_5=n_{\rm R}-n_{\rm L}$. Evaluated in thermal equilibrium using classical lattice techniques it reveals that the fluctuating soft fields indeed exhibit a rapid energy increase at early times and we observe a clear dependence of the diffusion rate of topological charge (sphaleron rate) on the the initial $n_5$, relevant in both early universe baryogenesis and relativistic heavy-ion collisions. The topological charge furthermore shows a drift among distinct vacuum sectors, roughly proportional to the initial $n_5$ and in turn the chiral imbalance is monotonously reduced as required by helicity conservation.