Off-shell higher-spin fields in $AdS_{4}$ and external currents

TL;DR

This paper develops an unfolded formulation for off-shell higher-spin fields in 4d anti-de Sitter space, coupling on-shell systems with external currents, and computes propagators using simplified operators.

Contribution

It introduces a novel unfolded system for off-shell higher-spin fields and external currents in AdS4, and provides a method to compute propagators directly from unfolded equations.

Findings

Constructed an unfolded system for off-shell higher-spin fields in AdS4.

Reformulated the system as Schwinger-Dyson equations for propagator calculation.

Identified operators that simplify the computation of wave equations.

Abstract

We construct an unfolded system for off-shell fields of arbitrary integer spin in 4d anti-de Sitter space. To this end we couple an on-shell system, encoding Fronsdal equations, to external Fronsdal currents for which we find an unfolded formulation. We present a reduction of the Fronsdal current system which brings it to the unfolded Fierz-Pauli system describing massive fields of arbitrary integer spin. Reformulating off-shell higher-spin system as the set of Schwinger-Dyson equations we compute propagators of higher-spin fields in the de Donder gauge directly from the unfolded equations. We discover operators that significantly simplify this computation, allowing a straightforward extraction of wave equations from an unfolded system.