Background Field Method and Generalized Field Redefinitions in Effective Field Theories

TL;DR

This paper investigates how radiative corrections induce non-linear redefinitions of background fields in spontaneously broken gauge theories, affecting renormalization and classical splitting, with special simplifications in Landau gauge.

Contribution

It demonstrates that background fields undergo gauge-invariant non-linear redefinitions due to quantum effects, crucial for gauge-independent renormalization in effective field theories.

Findings

Background fields are non-linearly redefined by radiative corrections.

Deformations of classical background-quantum splitting vanish in Landau gauge.

Redefinitions are essential for gauge-invariant renormalization of operators.

Abstract

We show that in a spontaneously broken effective gauge field theory, quantized in a general background $R_\xi$-gauge, also the background fields undergo a non-linear (albeit background-gauge invariant) field redefinition induced by radiative corrections. This redefinition proves to be crucial in order to renormalize the coupling constants of gauge-invariant operators in a gauge-independent way. The classical background-quantum splitting is also in general non-linearly deformed (in a non gauge-invariant way) by radiative corrections. Remarkably, such deformations vanish in the Landau gauge, to all orders in the loop expansion.