Renormalization of chiral perturbation theory with spinless matter field in curved spacetime

TL;DR

This paper extends chiral perturbation theory with spinless matter fields to curved spacetime, constructing the Lagrangian up to next-to-next-to-leading order and performing one-loop renormalization to identify divergences.

Contribution

It provides a systematic formulation and renormalization of chiral perturbation theory with spinless matter in curved spacetime, including curvature-induced terms.

Findings

Complete chiral Lagrangian up to $ ext{O}(p^3)$ in curved spacetime

Explicit calculation of ultraviolet divergences at one-loop level

Identification of curvature-induced terms in the renormalization process

Abstract

We generalize chiral perturbation theory with spinless matter fields in the fundamental representation of ${\rm SU}(N)$ to curved spacetime in the presence of an external gravitational field. This work is motivated by recent interest in investigating energy-momentum tensor matrix elements of matter fields. The complete chiral Lagrangian is constructed, including both minimal extensions from flat spacetime and new curvature-induced terms, up to the next-to-next-to-leading order in the chiral expansion, $\mathcal{O}(p^3)$. We perform a systematic one-loop renormalization of the generating functional using the background field method combined with the heat-kernel technique, and explicitly compute the resulting ultraviolet divergences.