Superfield Theories in Tensorial Superspaces and the Dynamics of Higher Spin Fields

TL;DR

This paper explores superfield formulations of higher spin equations in tensorial superspaces and finds that supergravity solutions are mostly trivial, indicating the need for extended frameworks to develop interacting higher spin theories.

Contribution

It introduces superfield generalizations of higher spin equations in tensorial superspaces and analyzes supergravity solutions, revealing their triviality and suggesting extensions for non-linear theories.

Findings

Most supergravity solutions are superconformally flat and OSp(1|n)-related.

These solutions cannot produce minimal coupling of higher spin fields.

Extended tensorial superspaces may be necessary for interacting higher spin theories.

Abstract

We present the superfield generalization of free higher spin equations in tensorial superspaces and analyze tensorial supergravities with GL(n) and SL(n) holonomy as a possible framework for the construction of a non-linear higher spin field theory. Surprisingly enough, we find that the most general solution of the supergravity constraints is given by a class of superconformally flat and OSp(1|n)-related geometries. Because of the conformal symmetry of the supergravity constraints and of the higher spin field equations such geometries turn out to be trivial in the sense that they cannot generate a `minimal' coupling of higher spin fields to their potentials even in curved backgrounds with a non-zero cosmological constant. This suggests that the construction of interacting higher spin theories in this framework might require an extension of the tensorial superspace with additional coordinates such as twistor-like spinor variables which are used to construct the OSp(1|2n) invariant (`preonic') superparticle action in tensorial superspace.