Background Field Method and Generalized Field Redefinitions in Effective Field Theories

TL;DR

This paper investigates non-linear background field redefinitions in effective gauge theories, highlighting their role in symmetric renormalization and how gauge choices influence these deformations at the quantum level.

Contribution

It provides a detailed analysis of quantum-induced non-linear background field redefinitions and their impact on the renormalization process in gauge theories.

Findings

Non-linear redefinitions are essential for symmetric renormalization.

In Landau gauge, deformations vanish at all loop orders.

Classical background-quantum splitting is deformed by radiative corrections.

Abstract

We study the non-linear background field redefinitions arising at the quantum level in a spontaneously broken effective gauge field theory. The non-linear field redefinitions are crucial for the symmetric (i.e. fulfilling all the relevant functional identities of the theory) renormalization of gauge-invariant operators. In a general $R_\xi$-gauge the classical background-quantum splitting is also non-linearly deformed by radiative corrections. In the Landau gauge these deformations vanish to all orders in the loop expansion.