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arXiv · 2502.03284

Finiteness of the Yang-Mills-Chern-Simons action in linear covariant gauges by taking into account gauge copies

Daniel O. R. Azevedo·Antonio D. Pereira
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Abstract

In recent years, the effects of removing infinitesimal Gribov copies from the path integral of gauge-fixed Yang-Mills-Chern-Simons theories formulated in three-dimensional Euclidean space have been investigated. Part of the interest resides on the fact that such an elimination of gauge copies introduces a mass parameter, the Gribov parameter, which is relevant when the assumptions of the Faddeev-Popov procedure are not well-grounded. Such a parameter enters the propagator of the gauge field which is topologically massive due to the Chern-Simons term. The resulting action, which eliminates infinitesimal Gribov copies in this context, has been constructed in linear covariant gauges and the interplay between the aforementioned mass-parameters allows for a rich phase diagram in which confining and deconfining signatures are observed in the gauge-field propagator. In the present work, we establish the renormalization properties of such a theory at all orders in perturbation theory by means of the algebraic renormalization framework and show that the removal of infinitesimal Gribov copies does not affect the standard non-renormalization properties of standard gauge-fixed Yang-Mills-Chern-Simons theories, i.e., the theory is finite.

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Daniel O. R. Azevedo, Antonio D. Pereira. 2025-02-05. Finiteness of the Yang-Mills-Chern-Simons action in linear covariant gauges by taking into account gauge copies. https://arxiv.org/abs/2502.03284

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