Supersymmetric electric-magnetic duality of hypergravity

TL;DR

This paper explores the electric-magnetic duality invariance in hypergravity, a higher-spin supersymmetric theory, by reformulating the free theory using prepotentials to make duality symmetry explicit, and discusses potential extensions to infinite higher-spin towers.

Contribution

It introduces a duality-invariant formulation of hypergravity using prepotentials, extending previous methods to higher spins and revealing the link between duality and conformal gauge symmetries.

Findings

Prepotential formulation makes duality invariance manifest.

The approach is consistent with previous spin-(3/2,2) results.

The formulation hints at a deep connection between duality and conformal invariance.

Abstract

Hypergravity is the theory in which the graviton, of spin-2, has a supersymmetric partner of spin-5/2. There are "no-go" theorems that prevent interactions in these higher spin theories. However, it appears that one can circumvent them by bringing in an infinite tower of higher spin fields. With this possibility in mind, we study herein the electric-magnetic duality invariance of hypergravity. The analysis is carried out in detail for the free theory of the spin-(2,5/2) multiplet, and it is indicated how it may be extended to the infinite tower of higher spins. Interactions are not considered. The procedure is the same that was employed recently for the spin-(3/2,2) multiplet of supergravity. One introduces new potentials ("prepotentials") by solving the constraints of the Hamiltonian formulation. In terms of the prepotentials, the action is written in a form in which its electric-magnetic duality invariance is manifest. The prepotential action is local, but the spacetime invariance is not manifest. Just as for the spin-2 and spin-(3/2,2) cases, the gauge symmetries of the prepotential action take a form similar to those of the free conformal theory of the same multiplet. The automatic emergence of gauge conformal invariance out of demand of manifest duality invariance, is yet another evidence of the subtle interplay between duality invariance and spacetime symmetry. We also compare and contrast the formulation with that of the analogous spin-(1,3/2) multiplet.