Higher Spins in Hyper-Superspace

TL;DR

This paper extends higher spin theory to hyper-superspaces, establishing superconformal transformations and relating correlation functions on flat hyper-superspaces to those on supergroup manifolds, advancing the understanding of supermultiplet structures.

Contribution

It introduces a framework for describing higher-spin supermultiplets in hyper-superspaces and relates correlation functions across different geometric settings using superconformal transformations.

Findings

Derived superconformal transformations linking flat and curved hyper-superspaces.

Established relations between correlation functions on flat hyperspace and supergroup manifolds.

Explicitly computed correlation functions for N=1, D=3 superconformal scalar supermultiplets.

Abstract

We extend the results of arXiv:1401.1645 on the generalized conformal Sp(2n)-structure of infinite multiplets of higher spin fields, formulated in spaces with extra tensorial directions (hyperspaces), to the description of OSp(1|2n)-invariant infinite-dimensional higher-spin supermultiplets formulated in terms of scalar superfields on flat hyper-superspaces and on OSp(1|n) supergroup manifolds. We find generalized superconformal transformations relating the superfields and their equations of motion in flat hyper-superspace with those on the OSp(1|n) supermanifold. We then use these transformations to relate the two-, three- and four-point correlation functions of the scalar superfields on flat hyperspace, derived by requiring the OSp(1|2n) invariance of the correlators, to correlation functions on the OSp(1|n) group manifold. As a byproduct, for the simplest particular case of a conventional N=1, D=3 superconformal theory of scalar superfields, we also derive correlation functions of component fields of the scalar supermultiplet including those of auxiliary fields.