Superfield continuous spin equations of motion

TL;DR

This paper develops a manifestly supersymmetric framework for continuous spin representations in 4D Minkowski superspace, unifying integer and half-integer helicities through superfield equations of motion.

Contribution

It introduces a superspace formulation for continuous spin representations, making supersymmetry and helicity connections explicit at the level of equations of motion.

Findings

Superfield equations reproduce Wigner's conditions for continuous spin.

Unified description of integer and half-integer helicities in superspace.

Manifest supersymmetry in continuous spin representation equations.

Abstract

We propose a description of %manifestly supersymmetric continuous spin representations in $4D,\mathcal{N}=1$ Minkowski superspace at the level of equations of motions. The usual continuous spin wave function is promoted to a chiral or a complex linear superfield which includes both the single-valued (span integer helicities) and the double-valued (span half-integer helicities) representations thus making their connection under supersymmetry manifest. The set of proposed superspace constraints for both superfield generate the expected Wigner's conditions for both representations.