Parity anomaly in four dimensions

Abstract

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 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.

Revtex, 7 pp V2: added remarks and references

References in corpus (2)

• Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface
• Induced parity-odd effective action for a Dirac field on $S^2\times S^1$

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