Superfield continuous spin equations of motion

We propose a description of manifestly supersymmetric continuous spin representations in 4D, 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. (C) 2019 The Author(s). Published by Elsevier B.V.