Background Harmonic Superfields in N=2 Supergravity

TL;DR

This paper extends the harmonic superfield formalism in N=2 supergravity by introducing background harmonic superfields with B-covariance, leading to new linear gravitational superfields and a perturbative supergravity action.

Contribution

It develops a modified harmonic superfield formalism with B-covariance, revealing new linear gravitational superfields and their relation to background superfields in N=2 supergravity.

Findings

Introduction of B-covariance leads to linear gravitational superfields.

Analytic prepotentials transform nonstandardly under background supersymmetry.

Perturbative supergravity action expanded in B-covariant superfields.

Abstract

A modification of the harmonic superfield formalism in $D=4, N=2$ supergravity using a subsidiary condition of covariance under the background supersymmetry with a central charge ($B$-covariance) is considered. Conservation of analyticity together with the $B$-covariance leads to the appearance of linear gravitational superfields. Analytic prepotentials arise in a decomposition of the background linear superfields in terms of spinor coordinates and transform in a nonstandard way under the background supersymmetry. The linear gravitational superfields can be written via spinor derivatives of nonanalytic spinor prepotentials. The perturbative expansion of the extended supergravity action in terms of the $B$-covariant superfields and the corresponding version of the differential-geometric formalism are considered. We discuss the dual harmonic representation of the linearized extended supergravity, which corresponds to the dynamical condition of Grassmann analyticity.