Quantum aspects of Yukawa model with scalar and axial scalar fields in curved spacetime

TL;DR

This paper investigates the quantum properties and renormalization of a Yukawa model with scalar and axial scalar fields in curved spacetime, deriving divergences, beta-functions, and the effective potential.

Contribution

It provides a detailed one-loop renormalization analysis of the Yukawa model with scalar and axial scalar fields in curved spacetime, including beta-functions and effective potential.

Findings

Derived one-loop divergences using heat-kernel technique

Calculated beta- and gamma-functions for all couplings

Constructed the renormalized effective potential up to linear curvature

Abstract

We study the Yukawa model with one scalar and one axial scalar fields, coupled to $N$ copies of Dirac fermions, in curved spacetime background. The theory possesses a reach set of coupling constants, including the scalar terms with odd powers of scalar fields in the potential, and constants of non-minimal coupling of the scalar fields to gravity. Using the heat-kernel technique and dimensional regularization, we derive the one-loop divergences, describe the renormalization of the theory under consideration and calculate the full set of beta- and gamma-functions for all coupling constants and fields. As a next step, we construct the renormalized one-loop effective potential of the scalar fields up to the terms linear in scalar curvature. This calculation includes only the contributions from quantum scalar fields, and is performed using covariant cut-off regularization and local momentum representation. Some difficulties of the renormalization group approach to the effective potential in the case under consideration are discussed.