U(N) spinning particles and higher spin fields on Kaehler backgrounds

TL;DR

This paper reviews the quantization of U(N) spinning particles on complex backgrounds, deriving higher spin field equations and analyzing their effective actions on Kaehler manifolds, with focus on (p,q)-forms and Hodge duality.

Contribution

It introduces a method to extend U(N) spinning particle models to Kaehler backgrounds and derives effective actions for (p,q)-forms, advancing higher spin field theory on complex manifolds.

Findings

Derived equations for higher spin fields on complex backgrounds.

Extended spinning particle models to Kaehler manifolds.

Computed one-loop effective actions for (p,q)-forms.

Abstract

In this short contribution we will review the quantization of U(N) spinning particles with complex target spaces, producing equations for higher spin fields on complex backgrounds. We will focus first on flat complex space, and subsequently discuss how to extend our model on suitable Kaehler manifolds. In the final section, we will specialize to (p,q)-forms on arbitrary Kaehler spaces and present their one-loop effective actions as well as issues related to Hodge duality.