Superembedding methods for 4d N-extended SCFTs

TL;DR

The paper generalizes superembedding methods to 4D SCFTs with extended supersymmetry by embedding into a six-dimensional space with symmetry $SU(2,2|\mathcal{N})$ and enforcing the projective light-cone constraint $X^2=0$, producing a linear action of the superconformal group. It constructs the $\mathcal{N}$-extended 4D superspace as a coset and derives the transformation rules for superfields, with explicit attention to the chiral sector and the emergence of chiral primaries. In the explicit $\mathcal{N}=2$ case, the chiral multiplet contains nine components organized according to the Pascal pyramid at layer $\mathcal{N}$, and the analysis is extended to $\mathcal{N}=4$ where the component count reaches 81. The framework provides a manifestly superconformal description applicable to conformally flat spaces and lays groundwork for correlators and non-holomorphic operators in extended SCFTs.

Abstract

We consider the embedding method of the superconformal group in four dimensions in the case of extended supersymmetry, hence generalizing the recent work of Goldberger, Skiba and Son which was restricted at N=1. Moreover, we work out explicitly the case of N=2 chiral superfields in four dimensions, putting the component fields in correspondence with Pascal's pyramid at layer N. This correspondence is a generic property of the N-extended chiral sector.

Figures (1)

• Figure 1: A few layers in the positive Pascal pyramid. The pyramid contains in principle also negative extensions, but they have been cut here. This picture has been taken from PyramidPicture.