Higher covariant derivative regulators and non-multiplicative renormalization

TL;DR

This paper demonstrates that combining higher covariant derivative regularization with dimensional regularization allows for consistent one-loop renormalization of 4D Yang-Mills theories, extending hybrid methods to divergent theories.

Contribution

It shows how hybrid regularization methods can be effectively applied to divergent theories like Yang-Mills, not just finite ones.

Findings

Higher covariant derivative regularization can be complemented with dimensional regularization.

Hybrid regularization methods are applicable to divergent theories.

Consistent one-loop renormalization of Yang-Mills achieved.

Abstract

The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with dimensional regularization to obtain a consistent renormalized 4-dimensional Yang-Mills theory at the one-loop level. This shows that hybrid regularization methods can be applied not only to finite theories, like \eg\ Chern-Simons, but also to divergent theories.