Higher Spin Superfield Interactions with the Chiral Supermultiplet: Conserved Supercurrents and Cubic Vertices

Abstract

Abstract:We investigate cubic interactions between a chiral superfield and higher spin superfields corresponding to irreducible representations of the 4D, N = 1 super-Poincaré algebra. We do this by demanding an invariance under the most general transformation, linear in the chiral superfield. Following Noether's method we construct an infinite tower of higher spin supercurrent multiplets which are quadratic in the chiral superfield and include higher derivatives. The results are that a single, massless, chiral superfield can couple only to the half-integer spin supermultiplets (s + 1, s + 1/2) and for every value of spin there is an appropriate improvement term that reduces the supercurrent multiplet to a minimal multiplet which matches that of superconformal higher spins. On the other hand a single, massive, chiral superfield can couple only to higher spin supermultiplets of type (2l + 2 , 2l + 3/2) (only odd values of s, s = 2l + 1) and there is no minimal multiplet. Furthermore, for the massless case we discuss the component level higher spin currents and provide explicit expressions for the integer and half-integer spin conserved currents together with a R-symmetry current.

Higher spin supersymmetry at the cosmological collider: sculpting SUSY rilles in the CMB

“…The result of that would be that, the spectrum of the half integer supermultiplet will collapse from (s + 1, s + 1/2, s + 1/2, s) to (s + 1, s + 1/2) and more importantly the generator of cubic interactions J α(s)α(s) in (18) will become conserved higher spin supercurrents. Such supercurrents have been found in [68][69][70][71][72][73][74][75][76] and their structure is consistent with (20). are explicitly after in this work.…”

“…Using this as a starting point, one can project the superspace Lagrangian to components and find the corresponding field theory (see [64,65] and detailed examples can be found in [29,69]). The result will include the entire spectrum of fields of the supersymmetric theory.…”

Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

“…Recent interesting discussion of higher-spin supersymmetric theories may be found in refs. [72][73][74].…”

Symmetries of supergravity backgrounds and supersymmetric field theory

“…(4.15), were described in [64,100,101] for the cases of Minkowski and AdS backgrounds. Various aspects of such non-conformal higher-spin supercurrents in Minkowski superspace were studied in [102][103][104]. It would be interesting to study consistent non-conformal deformations of other conformal supercurrents introduced in section 4.2.…”