The off-shell behaviour of propagators and the Goldstone field in higher spin gauge theory on $AdS_{d+1}$ space

TL;DR

This paper analyzes the structure, gauge dependence, and boundary behavior of propagators for higher spin gauge fields in $AdS$ space, clarifying the role of Goldstone modes and their relation to gauge fixing.

Contribution

It provides a detailed analysis of propagator structure and gauge dependence in higher spin $AdS$ gauge theories, fixing ambiguities through boundary conditions and representation theory.

Findings

Propagators' structure is fixed by boundary behavior.

Goldstone modes are linked to gauge fixing procedures.

Gauge dependence can be systematically characterized.

Abstract

A detailed analysis of the structure and gauge dependence of the bulk-to-bulk propagators for the higher spin gauge fields in $AdS$ space is performed. The possible freedom in the construction of the propagators is investigated and fixed by the correct boundary behaviour and correspondence to the representation theory results for the $AdS$ space isometry group. The classical origin of the Goldstone mode and its connection with the gauge fixing procedure is considered.