Background field formalism for chiral matter and gauge fields conformally coupled to supergravity

TL;DR

This paper develops a covariant, conformal background field formalism for chiral matter, gauge fields, and supergravity, enabling more efficient one-loop calculations without perturbative expansions in the inverse Planck scale.

Contribution

It extends the background field formalism to second order in supergravity and gauge prepotentials, including models with linear superfield compensators, advancing supergravity quantum computations.

Findings

First second-order covariant expansion in supergravity models

Framework applicable to models with linear superfield compensators

Facilitates one-loop calculations without inverse Planck scale expansion

Abstract

We expand the generic model involving chiral matter, super Yang-Mills gauge fields, and supergravity to second order in the gravity and gauge prepotentials in a manifestly covariant and conformal way. Such a class of models includes conventional chiral matter coupled to supergravity via a conformal compensator. This is a first step toward calculating one-loop effects in supergravity in a way that does not require a perturbative expansion in the inverse Planck scale or a recourse to component level calculations to handle the coupling of the K\"ahler potential to the gravity sector. We also consider a more restrictive model involving a linear superfield in the role of the conformal compensator and investigate the similarities it has to the dual chiral model.