Mixed Anomalies in 4 and 6 Dimensional Space with Torsion

Abstract

The chiral and the covariant Lorentz anomalies are evaluated by using the expansion coefficients of the heat kernel in the path integral method, when the fermion with spin 1/2 couples with the gauge, the gravitational and the torsion fields. In 4 and 6 dimensions, torsion tensors do not affect the index theorem because, in the chiral anomalies, the terms containing torsions are expressed as total divergence. It is however shown that the contribution of torsion tensors remains in the covariant Lorentz anomalies.