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

Rabin Banerjee·Shinichi Deguchi
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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.

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Rabin Banerjee, Shinichi Deguchi. 2005-09-21. A BRST gauge-fixing procedure for Yang-Mills theory on sphere. https://doi.org/10.1016/j.physletb.2005.10.067

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