On classical and quantum deformations of gauge theories

TL;DR

This paper extends the framework for gauge-invariant deformations of gauge theories, including quantum aspects, by constructing exact transformations for theories with open gauge algebras and relating their quantum effective actions.

Contribution

It introduces a method to construct exact gauge-invariant deformations for theories with open gauge algebras and explores their quantum implications.

Findings

Derived exact relations between quantum effective actions of deformed theories.

Constructed explicit gauge-invariant transformations for open gauge algebra theories.

Analyzed quantum effects of classical gauge deformations.

Abstract

We elaborate the generalizations of the approach to gauge-invariant deformations of the gauge theories developed in our previous work [1]. In the given paper we construct the exact transformations defying the gauge-invariant deformed theory on the base of initial gauge theory with irreducible open gauge algebra. Like in [1], for the theories with open gauge algebras these transformations are the shifts of the initial gauge fields $A \rightarrow A+h(A)$, with the help of the arbitrary and in general non-local functions $h(A)$. The results are applied to study the quantum aspects of the deformed theories. We derive the exact relation between the quantum effective actions for the above classical theories, where one is obtained from another with the help of the deformation.