Symmetries of the Dirac operator with skew-symmetric torsion

TL;DR

This paper explores how skew-symmetric torsion influences the symmetries of the Dirac operator, revealing new symmetry operators linked to generalized conformal Killing-Yano tensors in specific geometric contexts.

Contribution

It demonstrates that generalized conformal Killing-Yano tensors generate symmetry operators for the massless Dirac equation under torsion, with explicit conditions for anomaly cancellation.

Findings

Symmetries arise from generalized conformal Killing-Yano tensors.

Symmetries are established in strong KT and HKT manifolds.

An explicit anomaly condition is identified for symmetry operators.

Abstract

In this paper, we consider the symmetries of the Dirac operator derived from a connection with skew-symmetric torsion. We find that the generalized conformal Killing-Yano tensors give rise to symmetry operators of the massless Dirac equation, provided an explicitly given anomaly vanishes. We show that this gives rise to symmetries of the Dirac operator in the case of strong Kahler with torsion (KT) and strong hyper-Kahler with torsion (HKT) manifolds.