# Current Exchanges for Reducible Higher Spin Multiplets and Gauge Fixing

## TL;DR

This paper analyzes current exchanges in reducible higher spin field triplets, deriving propagators, decomposing into irreducible modes, and comparing gauge-fixed and gauge-invariant approaches for cubic interactions.

## Contribution

It provides a detailed method to decompose reducible higher spin triplet fields into irreducible Fronsdal fields and computes their current exchanges and propagators.

## Key findings

- Derived explicit propagators for reducible higher spin triplets.
- Showed how to decompose triplet fields into irreducible higher spin fields.
- Compared gauge-fixed and gauge-invariant formulations for simplicity.

## Abstract

We compute the current exchanges between triplets of higher spin fields which describe reducible representations of the Poincare group. Through this computation we can extract the propagator of the reducible higher spin fields which compose the triplet. We show how to decompose the triplet fields into irreducible HS fields which obey Fronsdal equations, and how to compute the current-current interaction for the cubic couplings which appear in ArXiv:0708.1399 [hep-th] using the decomposition into irreducible modes. We compare this result with the same computation using a gauge fixed (Feynman) version of the triplet Lagrangian which allows us to write very simple HS propagators for the triplet fields.