Superembedding methods for 4D N=1 SCFTs

Abstract

We extend the SO(4, 2) covariant lightcone embedding methods of four-dimensional CFTs to N = 1 superconformal field theory (SCFT). Manifest superconformal SU(2, 2 vertical bar 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 vertical bar 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 antichiral 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 antichiral fields. Superconformal expressions for the leading singularities in the operator product expansion of chiral and antichiral operators are also given. Because of covariance, our expressions should hold in any superconformally flat background, e. g., AdS(4) or R x S-3.