Chiral anomaly, induced current, and vacuum polarization tensor for a Dirac field in the presence of a defect

TL;DR

This paper calculates the vacuum polarization tensor and examines the chiral anomaly for a massless Dirac field with defects, showing that the anomaly remains unchanged and the induced current is exactly determined in specific dimensions.

Contribution

It provides a detailed evaluation of the vacuum polarization tensor in the presence of defects and demonstrates the invariance of the chiral anomaly under these conditions.

Findings

Chiral anomaly remains unchanged with defects in 1+1 and 3+1 dimensions.

Induced vacuum current in 1+1 dimensions is exactly determined by the lowest order VPT.

Vacuum polarization tensor is explicitly computed for a Dirac field with boundary conditions.

Abstract

We evaluate the vacuum polarization tensor (VPT) for a massless Dirac field in 1+1 and 3+1 dimensions, in the presence of a particular kind of defect, which in a special limit imposes bag boundary conditions. We also show that the chiral anomaly in the presence of such a defect is the same as when no defects are present, both in 1+1 and 3+1 dimensions. This implies that the induced vacuum current in 1+1 dimensions due to the lowest order VPT is exact.