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

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