Anomalous non-conservation of fermion/chiral number in Abelian gauge theories at finite temperature

TL;DR

This paper investigates how fermion number non-conservation occurs in Abelian gauge theories at finite temperature, revealing a higher-than-expected rate of chirality change due to gauge field fluctuations, with implications for cosmological phenomena.

Contribution

It provides the first numerical lattice simulation evidence showing enhanced fermion number non-conservation rates in Abelian theories, revising previous theoretical estimates.

Findings

Fermionic charge undergoes diffusive random walk in magnetic fields.

Numerical rate of chirality non-conservation is about 10 times larger than earlier estimates.

Revised understanding impacts theories of baryogenesis, magnetogenesis, and chiral symmetry evolution.

Abstract

We discuss the non-conservation of fermion number (or chirality breaking, depending on the fermionic charge assignment) in Abelian gauge theories at finite temperature. We study different mechanisms of fermionic charge disappearance in the high temperature plasma, using both analytical estimates and real-time classical lattice numerical simulations. We investigate the random walk of the Chern-Simons number $Q \propto \int d^4x F_{\mu\nu}{\tilde F}^{\mu\nu}$, and show that it has a diffusive behaviour in the presence of an external magnetic field $B$. This indicates that the mechanism for fermionic number non-conservation for $B \neq 0$, is due to fluctuations of the gauge fields, similarly as in the case of non-Abelian gauge theories. We determine numerically, with lattice simulations, the rate $\Gamma$ of chirality non-conservation associated with this diffusion. We find the rate to be a factor $\mathcal{O}(10)$ larger compared to previous theoretical estimates, what calls for a revision of the implications of Abelian fermion number and chirality non-conservation for baryogenesis, magnetogenesis and chiral symmetry evolution. An erratum can be found at the end of the manuscript, following the results obtained in JHEP 10 (2019) 142 (1904.11892 [hep-th]), which reduce our original claim in the discrepancy between theory and numerics by a factor $\sim 5-6$.