Superspace first order formalism, trivial symmetries and electromagnetic interactions of linearized supergravity

Abstract

We introduce a first order description of linearized non-minimal (n = −1) supergravity in superspace, using the unconstrained prepotential superfield instead of the conventionally constrained super one forms. In this description, after integrating out the connection-like auxiliary superfield of first-order formalism, the superspace action is expressed in terms of a single superfield which combines the prepotential and compensator superfields. We use this description to construct the supersymmetric cubic interaction vertex 3/2 − 3/2 − 1/2 which describes the electromagnetic interaction between two non-minimal supergravity multiplets (superspin Y = 3/2 which contains a spin 2 and a spin 3/2 particles) and a vector multiplet (superspin Y = 1/2 contains a spin 1 and a spin 1/2 particles). Exploring the trivial symmetries emerging between the two Y = 3/2 supermultiplets, we show that this cubic vertex must depend on the vector multiplet superfield strength. This result generalize previous results for non-supersymmetric electromagnetic interactions of spin 2 particles. The constructed cubic interaction generates non-trivial deformations of the gauge transformations.

Superspace BRST/BV Operators of Superfield Gauge Theories

“…An important class of such theories is the one with open symmetry algebras, meaning that the commutator of two symmetries generates trivial symmetries. In general, supersymmetric theories fall into this class, unless one considers theories with off-shell supersymmetry, like the ones that have superspace descriptions (see the relevant discussion in [11]).…”

Supersymmetric quantum chiral higher spin gravity

“…See[32][33][34][35][36][37][38][39][40] for Lorentz covariant constructions for supersymmetric vertices in various dimensions 3. Tree level scattering amplitudes for supersymmetric higher spin fields in the framework of higher spin-IKKT models were considered in[42].…”