  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.
