On conformal supergravity and harmonic superspace

TL;DR

This paper introduces a covariant harmonic superspace framework based on conformal supergravity, simplifying calculations and deriving the full component action for hyperkahler cone sigma models coupled to supergravity.

Contribution

It presents a new covariant approach to harmonic superspace that clarifies its connection to projective superspace and streamlines supergravity calculations.

Findings

Derived the full component action for hyperkahler cone sigma models in conformal supergravity.

Established a covariant superspace framework that simplifies supergravity computations.

Connected harmonic superspace with projective superspace in a transparent manner.

Abstract

This paper describes a fully covariant approach to harmonic superspace. It is based on the conformal superspace description of conformal supergravity and involves extending the supermanifold M^{4|8} by the tangent bundle of CP^1. The resulting superspace M^{4|8} x TCP^1 can be identified in a certain gauge with the conventional harmonic superspace M^{4|8} x S^2. This approach not only makes the connection to projective superspace transparent, but simplifies calculations in harmonic superspace significantly by eliminating the need to deal directly with supergravity prepotentials. As an application of the covariant approach, we derive from harmonic superspace the full component action for the sigma model of a hyperkahler cone coupled to conformal supergravity. Further applications are also sketched.