Continuous spin gauge field in (A)dS space

TL;DR

This paper develops a gauge-invariant Lagrangian formulation for totally symmetric continuous spin fields in (A)dS space, constructs gauge-fixed and BRST-invariant Lagrangians, and demonstrates the partition function equals one.

Contribution

It introduces a novel Lagrangian gauge invariant formulation for continuous spin fields in (A)dS space, including gauge fixing and BRST symmetry, and analyzes their partition functions.

Findings

Partition function of the continuous spin field equals one.

A simple gauge-fixed Lagrangian is derived using a de Donder-like gauge.

Various decoupling limits of the continuous spin field are studied.

Abstract

Totally symmetric continuous spin field propagating in (A)dS is studied. Lagrangian gauge invariant formulation for such field is developed. Lagrangian of continuous spin field is constructed in terms of double traceless tensor fields, while gauge transformations are constructed in terms of traceless gauge transformation parameters. de Donder like gauge condition that leads to simple gauge fixed Lagrangian is found. Gauge-fixed Lagrangian invariant under global BRST transformations is presented. The BRST Lagrangian is used for computation of a partition function. It is demonstrated that the partition function of the continuous spin field is equal to one. Various decoupling limits of the continuous spin field are also studied.