Current Exchanges for Reducible Higher Spin Multiplets and Gauge Fixing

TL;DR

This work develops a BRST-based framework to analyze reducible higher spin triplets and their decomposition into irreducible Fronsdal fields. It provides two complementary methods to obtain current exchanges: (i) decomposing the triplet into irreducible modes to derive propagators and (ii) gauge-fixing the triplet Lagrangian to obtain simple propagators directly. The authors demonstrate that both approaches yield consistent current exchanges, with explicit results for spins 2, 4, and the general spin s with h=s or h=s-2, and they show that only the physically relevant traces propagate in the s=s case. The analysis yields detailed normalizations for irreducible propagators and clarifies how gauge degrees of freedom can be systematically controlled, offering a path to extending the method to AdS and fermionic HS fields and to higher-order couplings.

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.