Renormalization of Nielsen Identities

TL;DR

This paper investigates how gauge-fixing parameters influence Green's functions in Yang-Mills theories, extending Nielsen identity analysis to generalized gauges and discussing conditions for effective potential homogeneity.

Contribution

It extends the renormalization analysis of Nielsen identities to generalized 't Hooft gauges in complex Yang-Mills theories with scalar fields.

Findings

Extended Nielsen identity analysis to generalized gauges.

Identified conditions for homogeneity of the effective potential.

Analyzed renormalization in theories with multiple gauge groups.

Abstract

We study renormalization of identities governing the dependence of 1PI Green's functions on gauge-fixing parameters. For general dimensionally regularized Yang-Mills theories with gauge groups being direct products of arbitrary compact simple Lie groups and U(1) groups coupled to scalar fields, we extend the well known analysis in Fermi gauges to the class of generalized 't Hoot gauges $R_{\xi,u}$, in which also symmetry under global gauge transformations is broken by the gauge-fixing procedure. We also discuss conditions ensuring homogeneity of the Nielsen identity satisfied by the effective potential.