Higher Spins from Nonlinear Realizations of $OSp(1|8)$

TL;DR

This paper explores the connection between higher spin theories and nonlinear realizations of the supergroup OSp(1|8), constructing covariant superfield equations and invariant actions that extend supergravity concepts.

Contribution

It introduces a realization of OSp(1|8) on a supermanifold, deriving covariant equations for higher spins and proposing invariant superfield actions with interactions.

Findings

Covariant superfield equations for all massless higher spins derived.

Construction of invariant superfield actions with interactions.

Relation between higher spin theory and nonlinear supergroup realizations established.

Abstract

We exhibit surprising relations between higher spin theory and nonlinear realizations of the supergroup $OSp(1|8)$, a minimal superconformal extension of N=1, 4D supersymmetry with tensorial charges. We construct a realization of $OSp(1|8)$ on the coset supermanifold $OSp(1|8)/SL(4,R)$ which involves the tensorial superspace $R^{(10|4)}$ and Goldstone superfields given on it. The covariant superfield equation encompassing the component ones for all integer and half-integer massless higher spins amounts to the vanishing of covariant spinor derivatives of the suitable Goldstone superfields, and, via Maurer-Cartan equations, to the vanishing of $SL(4,R)$ supercurvature in odd directions of $R^{(10|4)}$. Aiming at higher spin extension of the Ogievetsky-Sokatchev formulation of N=1 supergravity, we generalize the notion of N=1 chirality and construct first examples of invariant superfield actions involving a non-trivial interaction. Some other potential implications of $OSp(1|8)$ in the proposed setting are briefly outlined.