U(N) spinning particles and higher spin equations on complex manifolds

TL;DR

This paper derives higher spin equations on complex manifolds using a U(N)-extended spinning particle model, revealing new gauge structures and coupling conditions on Kaehler manifolds of constant holomorphic curvature.

Contribution

It introduces a novel formulation of higher spin equations on complex manifolds via a spinning particle approach, including gauge constraints and couplings to specific curved spaces.

Findings

Higher spin equations formulated on complex manifolds.

Gauge algebra is quadratic and related to nonlinear superconformal algebras.

Coupling to Kaehler manifolds of constant holomorphic curvature achieved.

Abstract

Guided by a spinning particle model with U(N)-extended supergravity on the worldline we derive higher spin equations on complex manifolds. Their minimal formulation is in term of gauge fields which satisfy suitable constraints. The latter can be relaxed by introducing compensator fields. There is an obstruction to define these systems on arbitrarily curved spaces, just as in the usual theory of higher spin fields, but we show how to couple them to Kaehler manifolds of constant holomorphic curvature. Quite interestingly, the first class gauge algebra defining the U(N) particles on these manifolds is quadratic and realizes the zero mode sector of certain nonlinear U(N) superconformal algebras introduced sometimes ago by Bershadsky and Knizhnik in 2D.