Interacting massive/massless continuous-spin fields and integer-spin fields

TL;DR

This paper develops a light-cone gauge approach to describe and analyze interactions of continuous-spin and integer-spin fields in flat space, providing explicit cubic vertices and simplifying the formulation compared to previous methods.

Contribution

It introduces a light-cone gauge vector superspace formulation for continuous-spin fields and derives complete cubic interaction vertices, including cross-interactions with integer-spin fields, for space-time dimensions greater than four.

Findings

Explicit cubic vertices for continuous-spin fields are obtained.

A simplified formulation compared to oscillator methods is presented.

The equivalence between light-cone gauge and Lorentz covariant formulations is demonstrated.

Abstract

In the framework of light-cone gauge approach, interacting continuous-spin fields and integer-spin fields propagating in flat space are studied. The continuous-spin fields are considered by using a light-cone gauge vector superspace formulation. Description of massive continuous-spin fields associated with the principal, complementary and discrete series is presented. For the massive continuous-spin fields of the principal and complementary series and massless continuous-spin fields, all parity-even cubic vertices realized as functions on the light-cone gauge vector superspace are obtained. Cubic vertices for a cross-interaction of massive/massless continuous spin fields and massive/massless integer-spin fields are also derived. These results for cubic vertices are complete for the dimensions of space-time greater than four. The use of the light-cone gauge vector superspace formulation considerably simplifies the cubic vertices as compared to the ones of oscillator formulation. Some cubic vertices realized as distributions are also found. Map between the oscillator formulation and the vector superspace formulation of the continuous-spin fields is explicitly described. An equivalence of the light-cone gauge and Lorentz covariant formulations of the free continuous-spin fields is also demonstrated.