Gravitational parity anomaly with and without boundaries

  • Maxim KurkovEmail author
  • Dmitri Vassilevich
Open Access
Regular Article - Theoretical Physics


In this paper we consider gravitational parity anomaly in three and four dimensions. We start with a re-computation of this anomaly on a 3D manifold without boundaries and with a critical comparison of our results to the previous calculations. Then we compute the anomaly on 4D manifolds with boundaries with local bag boundary conditions. We find, that gravitational parity anomaly is localized on the boundary and contains a gravitational Chern-Simons terms together with a term depending of the extrinsic curvature. We also discuss the main properties of the anomaly, as the conformal invariance, relations between 3D and 4D anomalies, etc.


Anomalies in Field and String Theories Chern-Simons Theories Field Theories in Lower Dimensions 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.CMCC, Universidade Federal do ABCSanto AndréBrazil
  2. 2.Dipartimento di Fisica “E. Pancini”Universita di Napoli “Federico II”NapoliItaly
  3. 3.INFN — Sezione di NapoliNapoliItaly
  4. 4.Department of PhysicsTomsk State UniversityTomskRussia

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