Spinning particles and higher spin fields on (A)dS backgrounds

TL;DR

This work links worldline O(N) spinning particle models to geometrical, curvature-based formulations of higher-spin fields on conformally flat and (A)dS backgrounds. Through canonical quantization, it shows how worldline constraints reproduce higher-spin curvatures and how these curvatures can be expressed in terms of gauge potentials via a compensator mechanism, connecting to the Fronsdal–Labastida framework. On (A)dS spaces the constraint algebra becomes quadratically deformed, yet remains consistent and yields explicit curvature–to–potential relations with Spin 2, 3, 4 detailed and general spin formulas. The results unify flat-space higher-spin equations with their curved-space generalizations and point to potential one-loop quantum analyses on curved backgrounds using the path integral approach.

Abstract

Spinning particle models can be used to describe higher spin fields in first quantization. In this paper we discuss how spinning particles with gauged O(N) supersymmetries on the worldline can be consistently coupled to conformally flat spacetimes, both at the classical and at the quantum level. In particular, we consider canonical quantization on flat and on (A)dS backgrounds, and discuss in detail how the constraints due to the worldline gauge symmetries produce geometrical equations for higher spin fields, i.e. equations written in terms of generalized curvatures. On flat space the algebra of constraints is linear, and one can integrate part of the constraints by introducing gauge potentials. This way the equivalence of the geometrical formulation with the standard formulation in terms of gauge potentials is made manifest. On (A)dS backgrounds the algebra of constraints becomes quadratic, nevertheless one can use it to extend much of the previous analysis to this case. In particular, we derive general formulas for expressing the curvatures in terms of gauge potentials and discuss explicitly the cases of spin 2, 3 and 4.