Gauge invariant Lagrangian formulation of massive higher spin fields in (A)dS_3 space

TL;DR

This paper develops a gauge-invariant Lagrangian framework for massive higher spin fields in 3D (A)dS space, introducing auxiliary fields and separated variables to simplify the formulation and enable potential interaction studies.

Contribution

It presents a novel gauge-invariant Lagrangian formulation for massive higher spins in (A)dS_3, including explicit Lagrangians, gauge transformations, and a method to reduce the field set using separated variables.

Findings

Explicit Lagrangians and gauge transformations derived.

Separated variables simplify the Lagrangian formulation.

Framework applicable to arbitrary integer spin fields.

Abstract

We develop the frame-like formulation of massive bosonic higher spins fields in the case of 3-dimensional $(A)dS$ space with the arbitrary cosmological constant. The formulation is based on gauge-invariant description by involving the Stueckelberg auxiliary fields. The explicit form of the Lagrangians and the gauge transformation laws are found. The theory can be written in terms of gauge-invariant objects similar to the massless theories, thus allowing us to hope to use the same methods for investigation of interactions. In the massive spin 3 field example we are able to rewrite the Lagrangian using the new the so-called separated variables, so that the study of Lagrangian formulation reduces to finding the Lagrangian containing only half of the fields. The same construction takes places for arbitrary integer spin field as well. Further working in terms of separated variables, we build Lagrangian for arbitrary integer spin and write it in terms of gauge-invariant objects. Also, we demonstrate how to restore the full set of variables, thus receiving Lagrangian for the massive fields of arbitrary spin in the terms of initial fields.