U(N|M) quantum mechanics on Kaehler manifolds

TL;DR

This paper explores U(N|M) supersymmetric quantum mechanics on Kaehler manifolds, analyzing symmetry structures and computing heat kernels to understand higher spin field equations in a quantum framework.

Contribution

It introduces a new class of models with U(N|M) symmetry on Kaehler manifolds and computes their heat kernels using operatorial methods.

Findings

Derived the symmetry algebra for these models.

Computed the heat kernel in the short time limit.

Linked models to higher spin field quantization.

Abstract

We study the extended supersymmetric quantum mechanics, with supercharges transforming in the fundamental representation of U(N|M), as realized in certain one-dimensional nonlinear sigma models with Kaehler manifolds as target space. We discuss the symmetry algebra characterizing these models and, using operatorial methods, compute the heat kernel in the limit of short propagation time. These models are relevant for studying the quantum properties of a certain class of higher spin field equations in first quantization.