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

TL;DR

This paper explores how spinning particle models with gauged supersymmetries can describe higher spin fields on (A)dS backgrounds, deriving geometrical equations and gauge potential formulations at quantum and classical levels.

Contribution

It extends the spinning particle approach to (A)dS spaces, analyzing constraint algebras and formulating higher spin equations in terms of curvatures and potentials.

Findings

Constraint algebra is linear on flat space, quadratic on (A)dS.

Derived formulas for curvatures in terms of gauge potentials.

Explicit analysis for spins 2, 3, and 4.

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.