Auxiliary fields rescaling in higher-derivative supergravity

TL;DR

This paper investigates how to properly normalize Einstein terms in higher-derivative supergravity with curvature squared terms, showing that a combination of Legendre transformation and Weyl rescaling is necessary for correct coupling to matter.

Contribution

It demonstrates that standard Weyl rescaling alone is insufficient and introduces a combined Legendre transformation and Weyl rescaling method for proper normalization in higher-derivative supergravity.

Findings

Proper normalization requires combined Legendre transformation and Weyl rescaling.

Standard Weyl rescaling alone does not yield a normalized Einstein term.

The method applies to supergravity coupled to general functions of superfields.

Abstract

We study higher--derivative supergravity with curvature squared terms in different bases. Performing a Weyl rescaling only on the metric or on all the superfield components does not allow to obtain a normalized kinetic Einstein term from a $\cR+\cR^2$ theory. It is necessary to combine a Legendre transformation and a Weyl rescaling on a $\cR+\cR^2$ theory to arrive at a theory of supergravity coupled to matter. This mechanism is applied to supergravity coupled to a general function $k(R,\BR,\Phi,\bar\Phi)$, where $R$ is one of the supergravity chiral superfields and $\Phi$ a chiral matter superfield.