Parity anomaly in four dimensions

  title={Parity anomaly in four dimensions},
  author={Maxim Kurkov and Dmitri Vassilevich},
  journal={Physical Review D},
In an analogy to the odd-dimensional case we define the parity anomaly as the part of the one-loop effective action for fermions associated with spectral asymmetry of the Dirac operator. This quantity is computed directly on four-dimensional manifolds with a boundary and related to the Chern-Simons current on the boundary. Despite a quite unusual Chern-Simons level obtained, the action is gauge invariant and passes all consistency checks. 

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  • Part. Diff. Eq. 15, 245 (1990). doi:10.1080/03605309908820686 D. V. Vassilevich, J. Math. Phys. 36, 3174 (1995) doi:10.1063/1.531021 [gr-qc/9404052]. T. P. Branson, P. B. Gilkey, K. Kirsten and D. V. Vassilevich, Nucl. Phys. B 563, 603