Effective action for the Yukawa model in curved spacetime

TL;DR

This paper analyzes the one-loop renormalization and effective action of a Yukawa model with scalar and fermion fields in curved spacetime, revealing anomalies related to axial currents and providing detailed renormalization group functions.

Contribution

It provides the first comprehensive calculation of one-loop renormalization group functions and effective action for a Yukawa model with non-minimal coupling in curved spacetime, including anomaly analysis.

Findings

Calculated all one-loop renormalization group functions.

Derived the effective action up to order R^2 in curvature.

Identified axial current anomaly related to fermion mass and chiral terms.

Abstract

We consider the one-loop renormalization of a real scalar field interacting with a Dirac spinor field in curved spacetime. A general Yukawa interaction is considered which includes both a scalar and a pseudoscalar coupling. The scalar field is assumed to be non-minimally coupled to the gravitational field and to have a general quartic self-interaction potential. All of the one-loop renormalization group functions are evaluated and in the special case where there is no mass scale present in the classical theory (apart from the fields) we evaluate the one-loop effective action up to and including order $R^2$ in the curvature. In the case where the fermion is massive we include a chiral term in $\gamma_5$ and we show that although the $\gamma_5$ term can be removed by a redefinition of the spinor field an anomaly in the effective action arises that is related to the familiar axial current anomaly.