Renormalization of six-dimensional Yang-Mills theory in a background gauge field

TL;DR

This paper investigates the one-loop renormalization of six-dimensional Yang-Mills theory using the background field method, revealing non-asymptotic freedom and gauge-invariant counterterms.

Contribution

It provides a detailed analysis of renormalization in 6D Yang-Mills theory, including gauge-invariant counterterms and implications for the beta function.

Findings

Counterterms are gauge-invariant and do not vanish on shell.

The theory is not asymptotically free.

Analysis extends to higher orders via BRST identities.

Abstract

Using the background field method, we study in a general covariant gauge the renormalization of the 6-dimensional Yang-Mills theory. This requires background gauge invariant counterterms, some of which do not vanish on shell. Such counterterms occur, even off-shell, with gauge-independent coefficients. The analysis is done at one loop order and the extension to higher orders is discussed by means of the BRST identities. We examine the behaviour of the beta function, which implies that this theory is not asymptotically free.