Superembedding Methods for Current Superfields

TL;DR

This work extends the 4D ${ m N}=1$ superconformal embedding-space formalism to fields in arbitrary ${ m SU}(2,2|1)$ representations, establishing a linear action on an embedding superspace and a precise Minkowski-limit map. It provides manifestly covariant, index-free expressions for two- and three-point functions involving conserved currents and the supercurrent, using a comprehensive set of embedding-space invariants and an efficient projection to 4D. By enforcing superconformal and Ward identities, the authors fix the correlator structures up to a handful of constants, which are tied to current normalization and anomalies, and verify consistency with known results. The index-free embedding-space approach streamlines the construction of covariant correlators for current multiplets and lays groundwork for extensions to higher supersymmetry and conformal-block techniques, with caveats about contact terms and explicit embedding-space formulations of conservation laws.

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.