Gauged Yukawa model in curved spacetime

TL;DR

This paper investigates the quantum effects of a Yukawa model involving scalar, gauge, and fermion fields in curved spacetime, deriving the effective action, counterterms, and renormalization group functions using advanced background field methods.

Contribution

It introduces a comprehensive calculation of the one-loop effective action for the Yukawa model in curved spacetime, including gradient and potential terms, and discusses anomalies related to chiral transformations.

Findings

Derived the pole parts of the effective action depending on the scalar background.

Calculated counterterms and renormalization group functions for the model.

Analyzed the anomaly arising from chiral transformations removing pseudoscalar mass.

Abstract

The Yukawa model in curved spacetime is considered. We consider a complex scalar field coupled to a $U(1)$ gauge field and also interacting with Dirac fields with a general Yukawa coupling. The local momentum space method is used to obtain the one-loop effective action and we adopt the gauge condition independent background field method introduced by Vilkovisky and DeWitt. The pole parts of the one-loop effective action that depend on the background scalar field, that we do not assume to be constant, are found and used to calculate the counterterms and to determine the relevant renormalization group functions. Terms in the effective action that involve the gradient terms in the scalar field as well as the effective potential are found in the case where the scalar field and Dirac fields are massless. We also discuss the anomaly that arises if the pseudoscalar mass term for the Dirac fermions is removed by a chiral transformation.