Abstract
mathcal{N} -extended massless arbitrary integer and half-integer spin supermultiplets in four dimensional flat space are studied in the framework of light-cone gauge formalism. For such multiplets, by using light-cone momentum superspace, we build unconstrained light-cone gauge superfield formulation. The superfield formulation is used to develop a superspace representation for all cubic interactions vertices of the mathcal{N} -extended massless supermultiplets. Our suitable treatment of the light-cone gauge superfields allows us to obtain attractively simple superspace representation for the cubic interaction vertices. Su- perspace realization of relativistic symmetries of the mathcal{N} -extended Poincaré superalgebra on space of interacting fields is also obtained.
Highlights
Bosonic massless fields obtained in refs. [12, 13].1 In this paper, we consider arbitrary spin N -extended massless supermultiplets with arbitrary N = 4N in the 4d flat space
We note that it is the formalism of unconstrained light-cone gauge superfields that provides us a possibility to build attractively simple expressions for cubic vertices and allows us to obtain the full classification of cubic interactions
We introduce our N -extended momentum superspace and provide the explicit description of light-cone gauge unconstrained superfields which are defined on such superspace
Summary
We present a complete system of equations required to determine the cubic interaction vertices unambiguously. N = 3, the kinematical symmetry equations can further be simplified in view of the following well known observation. Restricting to the value n = 3, we represent kinematical symmetry equations obtained in the previous section in terms of densities (4.5). We see that the kinematical and dynamical symmetry constraints for cubic densities amount to equations for densities (4.25), (4.26) and equations for the cubic vertex p−[3] (4.6), (4.11), (4.17). To determine the cubic densities unambiguously we need some additional requirement We refer to such requirement as light-cone dynamical principle. For the cubic vertex p−[3] = p−λ1λ2λ3 (PR, PL, Pθ, βa) , we found the following complete system of equations:. We think that it is worthwhile to apply our complete system of equations to study the cubic vertices of arbitrary spin N -extended supersymmetric theories
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