Symmetries of the Dirac operator with skew-symmetric torsion

Understand

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.