Gravitational parity anomaly with and without boundaries

• Main Authors: Maxim Kurkov, Dmitri Vassilevich
• Format: Article
• Language: English
• Published: SpringerOpen 2018-03-01
• Series: Journal of High Energy Physics
• Subjects: Anomalies in Field and String Theories; Chern-Simons Theories; Field Theories in Lower Dimensions
• Online Access: http://link.springer.com/article/10.1007/JHEP03(2018)072

Abstract 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.