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Uniformizing higher-spin equations

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 Added by Maxim Grigoriev
 Publication date 2014
  fields Physics
and research's language is English




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Vasilievs higher-spin theories in various dimensions are uniformly represented as a simple system of equations. These equations and their gauge invariances are based on two superalgebras and have a transparent algebraic meaning. For a given higher-spin theory these algebras can be inferred from the vacuum higher-spin symmetries. The proposed system of equations admits a concise AKSZ formulation. We also discuss novel higher-spin systems including partially-massless and massive fields in AdS, as well as conformal and massless off-shell fields.



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We give an explicit superspace construction of higher spin conserved supercurrents built out of $4D,mathcal{N}=1$ massless supermultiplets of arbitrary spin. These supercurrents are gauge invariant and generate a large class of cubic interactions between a massless supermultiplet with superspin $Y_1=s_1+1/2$ and two massless supermultiplets of arbitrary superspin $Y_2$. These interactions are possible only for $s_1geq 2Y_2$. At the equality, the supercurrent acquires its simplest form and defines the supersymmetric, higher spin extension of the linearized Bel-Robinson tensor.
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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