Abstract
We focus on the geometrical reformulation of free higher spin supermultiplets in $4\rm{D},~\mathcal{N}=1$ flat superspace. We find that there is a de Wit-Freedman like hierarchy of superconnections with simple gauge transformations. The requirement for sensible free equations of motion imposes constraints on the gauge parameter superfields. Unlike the nonsupersymmetric case, we find several different constraints that can decouple the higher superconnections. By lifting these constraints nongeometrically via compensators we recover all known descriptions of arbitrary integer and half-integer gauge supermultiplets. In the constrained formulation we find a new description of half-integer supermultiplets, generalizing the new-minimal and virial formulations of linearized supergravity to higher spins. However this description can be formulated using compensators. The various descriptions can be labeled as geometrical or nongeometrical if the equations of motion can be expressed purely in terms of superconnections or not.
Highlights
The study of higher spins plays a special role in the search for underlying principles and symmetries of nature
Most of the progress done in higher-spin theories falls under two categories: (i) constructing consistent interactions involving higher spin gauge fields and (ii) the geometrical reformulation of free higher spins on Minkowski and anti–de Sitter (AdS) backgrounds
The correlation between these two directions is evident in the case of gravity, where the geometrical formulation of
Summary
The study of higher spins plays a special role in the search for underlying principles and symmetries of nature. We study the properties of a set of natural objects which define the notion of generalized higher spin superconnection and the corresponding supercurvature superfield We find that these objects arrange into a hierarchy ala de Wit and Freedman [54] in superspace. Demanding sensible superspace equations of motion for free theory, generates a variety of nonequivalent constraints that one can impose on the gauge parameter superfield. VI, the analysis is repeated for the ðs þ 1=2; sÞ class of supermultiplets described by a fermionic gauge superfield In this case there are two independent hierarchies, with s and s þ 1 members respectively and use them to generate all appropriate constraints in order to extract free equations of motion
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