Superembedding Methods for Current Superfields

TL;DR

This paper extends the superembedding formalism to arbitrary representations in 4D N=1 SCFTs, providing new covariant expressions for correlators involving conserved currents, enhancing the understanding of superconformal symmetry in field theories.

Contribution

The authors develop a superembedding formalism for arbitrary representations in 4D N=1 SCFTs, yielding new manifestly covariant correlator expressions for conserved currents.

Findings

Derived covariant two- and three-point functions involving conserved currents.

Presented a compact, index-free formalism for superembedding calculations.

Confirmed consistency with existing literature while introducing new covariant forms.

Abstract

We extend the superembedding formalism for 4D N=1 superconformal field theory (SCFT) to the case of fields in arbitrary representations of the superconformal group SU(2,2|1). As applications we obtain manifestly superconformally covariant expressions for two- and three-point functions involving conserved currents, e.g. the supercurrent multiplet or global symmetry current superfields. The embedding space results are presented in a compact form by employing an index-free formalism. Our expressions are consistent with the literature, but the manifestly covariant forms of correlators presented here are new.