# Chiral Anomaly and Schwinger Effect in Non-Abelian Gauge Theories

## TL;DR

This paper investigates how chiral fermions are produced in strong non-abelian gauge fields with non-zero Chern-Pontryagin density, extending Landau level analysis to non-abelian theories and exploring implications for chiral anomaly and backreaction in chromo-natural inflation.

## Contribution

It extends the Landau level analysis of fermion production to non-abelian gauge fields and examines the failure of vacuum subtraction in reproducing the chiral anomaly.

## Key findings

- Asymmetric fermion production reproduces the chiral anomaly.
- Vacuum subtraction scheme fails in non-abelian gauge theories.
- Backreaction includes vacuum corrections and fermion-induced currents.

## Abstract

We study the production of chiral fermions in a background of a strong non-abelian gauge field with a non-vanishing Chern-Pontryagin density. We discuss both pair production analogous to the Schwinger effect as well as asymmetric production through the chiral anomaly, sourced by the Chern-Pontryagin density. In abelian gauge theories one may nicely understand these processes by considering that the fermion dispersion relation forms discrete Landau levels. Here we extend this analysis to a non-abelian gauge theory, considering an intrinsically non-abelian isotropic and homogeneous SU(2) gauge field background with a non-vanishing Chern-Pontryagin density. We show that the asymmetric fermion production, together with a non-trivial vacuum contribution, correctly reproduces the chiral anomaly. This indicates that the usual vacuum subtraction scheme, imposing normal ordering, fails in this case. As a concrete example of this gauge field background, we consider chromo-natural inflation. Applying our analysis to this particular model, we compute the backreaction of the generated fermions on the gauge field background. This backreaction receives contributions both from the vacuum through a Coleman-Weinberg-type correction and from the fermion excitations through an induced current.