From Diophantus to Supergravity and massless higher spin multiplets

Abstract

We present a new method of deriving the off-shell spectrum of supergravity and massless $4D,\mathcal{N}=1$ higher spin multiplets without the need of an action and based on a set of natural requirements: (a.) existence of an underlying superspace description, (b.) an economical description of free, massless, higher spins and (c.) equal numbers of bosonic and fermionic degrees of freedom. We prove that for any theory that respects the above, the fermionic auxiliary components come in pairs and are gauge invariant and there are two types of bosonic auxiliary components. Type (1) are pairs of a $(2,0)$-tensor with real or imaginary $(1,1)$-tensor with non-trivial gauge transformations. Type (2) are singlets and gauge invariant. The outcome is a set of Diophantine equations, the solutions of which determine the off-shell spectrum of supergravity and massless higher spin multiplets. This approach provides (i) a classification of the irreducible, supersymmetric, representations of arbitrary spin and (ii) a very clean and intuitive explanation to why some of these theories have more than one formulations (e.g. the supergravity multiplet) and others do not.

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Cited by in corpus (13)

• Higher Spin Supersymmetry at the Cosmological Collider: Sculpting SUSY Rilles in the CMB
• Higher Spin Dark Matter
• Progress on cubic interactions of arbitrary superspin supermultiplets via gauge invariant supercurrents
• Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions
• Unconstrained off-shell superfield formulation of $4D,\mathcal{N}=2$ supersymmetric higher spins
• Interaction of supersymmetric nonlinear sigma models with external higher spin superfields via higher spin supercurrents
• Higher Spin Superfield interactions with Complex linear Supermultiplet: Conserved Supercurrents and Cubic Vertices
• Integer superspin supercurrents of matter supermultiplets
• Superspace formulation of massive half-integer superspin
• Hierarchy of Supersymmetric Higher Spin Connections
• Towards A Direct Detection of the Spin of Dark Matter
• Superspace First Order Formalism, Trivial Symmetries and Electromagnetic Interactions of Linearized Supergravity
• Lagrangian formulation of free arbitrary N-extended massless higher spin supermultiplets in 4D, AdS space