Comments on Nonlinear Sigma Models Coupled to Supergravity

TL;DR

This paper analyzes how nonlinear realizations of local supersymmetry in N=1, D=4 supergravity affect the geometry of sigma models, especially the elimination of scalar degrees of freedom and the positivity of the metric.

Contribution

It demonstrates that the sigma model metric remains positive semidefinite despite nonlinear supersymmetry effects, clarifying geometric properties in supergravity models.

Findings

Nonlinear realization can eliminate scalar degrees of freedom.

Sigma model metric remains positive semidefinite.

Effect on inflaton's scalar superpartner.

Abstract

N=1, D=4 non linear sigma models, parametrized by chiral superfields, usually describe Kaehlerian geometries, provided that Einstein frame supergravity is used. The sigma model metric is no longer Kaehler when local supersymmetry becomes nonlinearly realized through the nilpotency of the supergravity auxiliary fields. In some cases the nonlinear realization eliminates one scalar propagating degree of freedom. This happens when the sigma model conformal-frame metric has co-rank 2. In the geometry of the inflaton, this effect eliminates its scalar superpartner. We show that the sigma model metric remains semidefinite positive in all cases, due the to positivity properties of the conformal-frame sigma model metric.