Off-shell cubic hypermultiplet couplings to $\mathcal{N}=2$ higher spin gauge superfields

Abstract

We construct manifestly 4D, N = 2 supersymmetric and gauge invariant offshell cubic couplings of matter hypermultiplets to the higher integer spin gauge N = 2 multiplets introduced in arXiv:2109.07639 [hep-th]. The hypermultiplet is described by an analytic harmonic 4D, N = 2 superfield q + with the physical component spins s = ( 1 2 , 0) and an infinite number of auxiliary fields. The cubic coupling constructed has the schematic structure q + Ĥ++ (s) q + , where Ĥ++ (s) is a differential analytic operator of the highest degree (s − 1) accommodating the massless gauge N = 2 multiplet with the highest spin s. For odd s the gauge group generators and couplings are proportional to U(1) P G generator of the internal SU(2) P G symmetry of the hypermultiplet and so do not exist if SU(2) P G is unbroken. If this U(1) P G is identified with the central charge of 4D, N = 2 supersymmetry, a mass for the hypermultiplet is generated and the odd s couplings vanish in the proper massless limit. For even s the higher-spin gauge transformations and cubic superfield couplings can be defined for both massive and massless (central-charge neutral) hypermultiplets without including U(1) P G generator. All these features directly extend to the case of n hypermultiplets with the maximal internal symmetry USp(2n) × SU(2).

Cubic interactions of arbitrary spin fields in 3d flat space

“…The discussion of various methods for building interaction vertices in supersymmetric theories may be found in Refs. [37]- [43]. iv) In this paper, we studied cubic vertices of massive and massless fields.…”

On interactions of massless spin 3 and scalar fields

“…Notice that in[22] N = 2 supersymmetric generalization of cubic vertices containing in bosonic sector interactions of spin 0 field with massless integer spin s fields has been considered.…”

Conformal Interactions Between Matter and Higher‐Spin (Super)Fields

“…Once j A is known, the associated gauge multiplet of fields Υ A (the Weyl multiplet) is determined via the Noether coupling S NC = ∫ d𝜇 Υ A j A . This procedure is concisely described by Bergshoeff et al [36] In superspace, the Noether procedure was used, e.g., in [37][38][39] for ordinary supersymmetric theories, and more recently in [40][41][42][43][44] and [45] for  = 1 and  = 2 supersymmetric higher-spin theories in Minkowski superspace respectively. Refs.…”