Superembedding methods for 4d N=1 SCFTs

TL;DR

This paper develops a superembedding formalism for 4D N=1 SCFTs that simplifies the computation of correlation functions and superconformal invariants, applicable in various backgrounds like AdS_4.

Contribution

It introduces a covariant superembedding approach for 4D N=1 SCFTs that automatically solves Ward identities and provides compact, invariant expressions for correlators and OPE singularities.

Findings

Derived new expressions for correlation functions with chiral and anti-chiral superfields.

Provided manifestly invariant superconformal cross-ratios for four-point functions.

Presented superconformal expressions for leading OPE singularities.

Abstract

We extend SO(4,2) covariant lightcone embedding methods of four-dimensional CFTs to N=1 superconformal field theory (SCFT). Manifest superconformal SU(2,2|1) invariance is achieved by realizing 4D superconformal space as a surface embedded in the projective superspace spanned by certain complex chiral supermatrices. Because SU(2,2|1) acts linearly on the ambient space, the constraints on correlators implied by superconformal Ward identities are automatically solved in this formalism. Applications include new, compact expressions for correlation functions containing one anti-chiral superfield and arbitrary chiral superfield insertions, and manifestly invariant expressions for the superconformal cross-ratios that parametrize the four-point function of two chiral and two anti-chiral fields. Superconformal expressions for the leading singularities in the OPE of chiral and anti-chiral operators are also given. Because of covariance, our expressions are valid in any superconformally flat background, e.g., AdS_4 or R times S^3.