Supersymmetric electric-magnetic duality of hypergravity

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.

References in corpus (14)

• Duality Symmetric Actions
• Higher Spin Gauge Theories: Star-Product and AdS Space
• How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
• Duality, Self-Duality, Sources and Charge Quantization in Abelian N-Form Theories
• Duality in linearized gravity
• Elements of Vasiliev theory
• Duality invariance of all free bosonic and fermionic gauge fields
• Gravitational duality near de Sitter space
• E7(7) invariant Lagrangian of d=4 N=8 supergravity
• The Action for Twisted Self-Duality
• Duality invariance implies Poincare invariance
• Gravitational Electric-Magnetic Duality, Gauge Invariance and Twisted Self-Duality
• Twisted Self-Duality for Linearized Gravity in D dimensions
• Supersymmetric electric-magnetic duality as a manifest symmetry of the action for super-Maxwell theory and linearized supergravity

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• The Action of the (free) $(4,0)$-theory
• Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields
• Prepotentials for linearized supergravity
• Aspects of electric-magnetic dualities in maximal supergravity
• New Reflections on Gravitational Duality