Multiplicative renormalizability of Yang-Mills theory with the background field method in the BV-formalism

TL;DR

This paper investigates the gauge-invariant renormalizability of 4D Yang-Mills theory using the background field method and BV-formalism, showing it is quasimultiplicatively renormalizable in the physical sector.

Contribution

It introduces antifield partners to background fields and parameters, deriving a classical master-equation homogeneous in the BV formalism, and analyzes the renormalizability properties.

Findings

The model can be renormalized with standard counterterms.

It does not have exact multiplicative renormalizability.

It exhibits quasimultiplicative renormalizability in the physical sector.

Abstract

Studying the gauge-invariant renormalizability of four-dimensional Yang-Mills theory using the background field method and the BV-formalism, we derive a classical master-equation homogeneous with respect to the antibracket by introducing antifield partners to the background fields and parameters. The constructed model can be renormalized by the standard method of introducing counterterms. This model does not have (exact) multiplicative renormalizability but it does have this property in the physical sector (quasimultiplicative renormalizability).