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Register a new userInteger superspin supercurrents of matter supermultiplets
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Added by
Konstantinos Koutrolikos
Publication date
2018
fields
Physics
and research's language is
English
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In recent papers we demonstrated that consistent and non-trivial emph{linear} transformations of matter supermultiplets generate half-integer superspin supercurrents and the cubic interactions between matter and half-integer superspin supermultiplets. In this work we show that consistent and non-trivial emph{antilinear} transformations of matter superfields lead to the construction of integer superspin supercurrents and the cubic interactions between mater and integer superspin supermultiplets. Applying Noethers method to these transformations, we find new integer superspin supercurrents for the case of a free massless chiral superfield. Furthermore, we use them to find new integer superspin supercurrent multiplets for a massive chiral superfield and a chiral superfield with a linear superpotential. Also various selection rules for such interactions are found.
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We consider cubic interactions of the form $s-Y-Y$ between a massless integer superspin $s$ supermultiplet and two massless arbitrary integer or half integer superspin $Y$ supermultiplets. We focus on non-minimal interactions generated by gauge invariant supercurrent multiplets which are bilinear in the superfield strength of the superspin $Y$ supermultiplet. We find two types of consistent supercurrents. The first one corresponds to conformal integer superspin $s$ supermultiplets, exist only for even values of $s, s=2ell+2$, for arbitrary values of $Y$ and it is unique. The second one, corresponds to Poincare integer superspin $s$ supermultiplets, exist for arbitrary values of $s$ and $Y$.
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.
An explicit form for the lagrangian of an arbitrary half-integer superspin ${textsf{Y}}=s+1/2$ supermultiplet is obtained in $4{rm D},~mathcal{N}=1$ superspace. This is accomplished by the introduction of a tower of pairs of auxiliary superfields of increasing rank which are required to vanish on-shell for free theories. In the massless limit almost all auxiliary superfields decouple except one, which plays the role of compensator as required by the emergent gauge redundancy of the Lagrangian description of the massless theory. The number of off-shell degrees of freedom carried by the theory is $frac{8}{3}(s+1)(4s^2+11s+3)$.
Free massless higher-superspin superfields on the N=1, D=4 anti-de Sitter superspace are introduced. The linearized gauge transformations are postulated. Two families of dually equivalent gauge-invariant action functionals are constructed for massless half-integer-superspin s+1/2 (s >= 2) and integer-superspin s (s >= 1) superfields. For s=1, one of the formulations for half-integer superspin multiplets reduces to linearized minimal N=1 supergravity with a cosmological term, while the other is the lifting to the anti-de Sitter superspace of linearized non-minimal n=-1 supergravity.
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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