The gravitational chiral anomaly of spin-1/2 field in the presence of twisted boundary conditions for ordinary field theory

TL;DR

This paper investigates the gravitational chiral anomaly of spin-1/2 fields under twisted boundary conditions using supersymmetric quantum mechanics, extending the index theorem to account for discrete symmetries on manifolds.

Contribution

It introduces a Feynman diagram approach to compute anomalies in the presence of twisted boundary conditions, generalizing the G-index theorem for spin complexes.

Findings

Derived the chiral anomaly near fixed point spaces with discrete symmetry actions.

Confirmed the consistency of the Feynman diagram approach with the generalized index theorem.

Extended the understanding of anomalies in twisted boundary condition scenarios.

Abstract

We calculate the chiral anomaly in the neighbourhood of the fixed point space M_h which is constructed by the group action of a discrete symmetry h on a compact manifold M. The Feynman diagrams approach for the corresponding supersymmetric quantum mechanical system with twisted boundary conditions is used. The result we derive in this way agrees with the generalization of the ordinary index theorem (the G-index theorem) on the spin complex.