Superspace Gauge Fixing in Yang-Mills Matter Coupled Conformal Supergravity

TL;DR

This paper constructs a Yang-Mills matter coupled supergravity system in four-dimensional conformal superspace, analyzing two gauge-fixing procedures to connect superconformal and Poincaré supergravity formalisms.

Contribution

It introduces a detailed analysis of gauge-fixing procedures in superspace, clarifying the correspondence between superconformal and Poincaré supergravity formulations.

Findings

Two gauge-fixing procedures are explicitly analyzed.

The correspondence between superconformal and Poincaré supergravity is clarified.

The supergravity system with Yang-Mills matter coupling is constructed in conformal superspace.

Abstract

In $D=4$, $\cal{N}=1$ conformal superspace, the Yang-Mills matter coupled supergravity system is constructed where the Yang-Mills gauge interaction is introduced by extending the superconformal group to include the K\"ahler isometry group of chiral matter fields. There are two gauge-fixing procedures to get to the component Poincar\'e supergravity: one via the superconformal component formalism and the other via the Poincar\'e superspace formalism. These two types of superconformal gauge-fixing conditions are analyzed in detail and their correspondence is clarified.