Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

TL;DR

This paper develops a light-cone gauge formulation for continuous-spin fields in flat space, explicitly constructs all parity-invariant cubic interaction vertices involving these fields and arbitrary spin massive fields, and shows certain interactions are impossible.

Contribution

It provides the first explicit classification of cubic interaction vertices for continuous-spin and arbitrary spin massive fields in flat space.

Findings

Explicit list of parity-invariant cubic vertices involving continuous-spin and massive fields.

Proof that continuous-spin massless fields cannot interact with massless fields.

Development of a light-cone gauge framework for these interactions.

Abstract

Light-cone gauge formulation of relativistic dynamics of a continuous-spin field propagating in the flat space is developed. Cubic interaction vertices of continuous-spin massless fields and totally symmetric arbitrary spin massive fields are studied. We consider parity invariant cubic vertices that involve one continuous-spin massless field and two arbitrary spin massive fields and parity invariant cubic vertices that involve two continuous-spin massless fields and one arbitrary spin massive field. We construct the complete list of such vertices explicitly. Also we demonstrate that there are no cubic vertices describing consistent interaction of continuous-spin massless fields with arbitrary spin massless fields.