Mixed-symmetry continuous-spin fields in flat and AdS spaces

TL;DR

This paper develops a light-cone gauge framework for mixed-symmetry continuous-spin fields in flat and AdS spaces, deriving their actions, symmetry realizations, and spin operator structures, including for triplectic fields.

Contribution

It introduces a new light-cone gauge approach for mixed-symmetry continuous-spin fields in both flat and AdS spaces, detailing their actions and symmetry realizations.

Findings

Light-cone gauge actions for mixed-symmetry continuous-spin fields are derived.

Realization of relativistic symmetries on these fields is presented.

Spin operators are characterized as first- or second-order differential operators depending on the space.

Abstract

In the framework of light-cone gauge approach, bosonic and fermionic mixed-symmetry continuous-spin fields in AdS space and flat space are considered. For such fields, the light-cone gauge actions are found. Realization of relativistic symmetries of AdS and flat spaces on the continuous-spin fields is also presented. Simple realization of spin operators is found. With respect to vector variable entering the continuous-spin fields, the spin operators for the fields in flat space turn out to be first-order differential operators, while, for the the fields in AdS space, the spin operators are realized as the second-order differential operators. By product, we obtain also the simple description of triplectic mixed-symmetry continuous-spin fields.