A BRST gauge-fixing procedure for Yang-Mills theory on sphere

TL;DR

This paper develops a systematic BRST gauge-fixing procedure for Yang-Mills theory on an n-dimensional sphere, addressing issues with previous conditions and ensuring consistency with flat space equations in the large radius limit.

Contribution

It introduces a suitable gauge condition for Yang-Mills theory on a hypersphere and applies the BRST gauge-fixing procedure to derive consistent covariant field equations.

Findings

Proposed a gauge condition equivalent to Adler's but suitable for BRST formalism.

Derived covariant field equations for Yang-Mills fields on the hypersphere.

Reproduced flat space equations in the large radius limit.

Abstract

A gauge-fixing procedure for the Yang-Mills theory on an n-dimensional sphere (or a hypersphere) is discussed in a systematic manner. We claim that Adler's gauge-fixing condition used in massless Euclidean QED on a hypersphere is not conventional because of the presence of an extra free index, and hence is unfavorable for the gauge-fixing procedure based on the BRST invariance principle (or simply BRST gauge-fixing procedure). Choosing a suitable gauge condition, which is proved to be equivalent to a generalization of Adler's condition, we apply the BRST gauge-fixing procedure to the Yang-Mills theory on a hypersphere to obtain consistent results. Field equations for the Yang-Mills field and associated fields are derived in manifestly O(n+1) covariant or invariant forms. In the large radius limit, these equations reproduce the corresponding field equations defined on the n-dimensional flat space.