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Register a new userHierarchy of Supersymmetric Higher Spin Connections
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Added by
Konstantinos Koutrolikos
Publication date
2020
fields
Physics
and research's language is
English
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We focus on the geometrical reformulation of free higher spin supermultiplets in $4rm{D},~mathcal{N}=1$ 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.
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We consider a four dimensional generalized Wess-Zumino model formulated in terms of an arbitrary K{a}hler potential $mathcal{K}(Phi,bar{Phi})$ and an arbitrary chiral superpotential $mathcal{W}(Phi)$. A general analysis is given to describe the possible interactions of this theory with external higher spin gauge superfields of the ($s+1,s+1/2$) supermultiplet via higher spin supercurrents. It is shown that such interactions do not exist beyond supergravity $(sgeq2)$ for any $mathcal{K}$ and $mathcal{W}$. However, we find three exceptions, the theory of a free massless chiral, the theory of a free massive chiral and the theory of a free chiral with linear superpotential. For the first two, the higher spin supercurrents are known and for the third one we provide the explicit expressions. We also discuss the lower spin supercurrents. As expected, a coupling to (non-minimal) supergravity ($s=1$) can always be found and we give the generating supercurrent and supertrace for arbitrary $mathcal{K}$ and $mathcal{W}$. On the other hand, coupling to the vector supermultiplet ($s=0$) is possible only if $mathcal{K}=mathcal{K}(bar{Phi}Phi)$ and $mathcal{W}=0$.
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