Atiyah–Patodi–Singer index theorem for domain walls. (3rd July 2020)

• Record Type: Journal Article
• Authors: Ivanov, A V; Vassilevich, D V
• Is Part Of: Journal of physics. Volume 53:Number 30(2020)
• Publication Date: 2020-07-03
• Subjects: index theorem -- anomalies -- heat kernel expansion -- domain walls; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab9385
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We consider the index of a Dirac operator on a compact even dimensional manifold with a domain wall. The latter is defined as a co-dimension one submanifold where the connection jumps. We formulate and prove an analog of the Atiyah–Patodi–Singer theorem that relates the index to the bulk integral of Pontryagin density and η -invariants of auxiliary Dirac operators on the domain wall. Thus the index is expressed through the global chiral anomaly in the volume and the parity anomaly on the wall.