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

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.