Atiyah-Patodi-Singer index theorem for domain walls

Author(s)

Ivanov, V, A. ; Vassilevich, D. V. ^{[1, 2]}

Affiliation

^[1] Univ Fed ABC, Ctr Math Computat & Cognit, BR-09210580 Santo Andre, SP - Brazil

^[2] Tomsk State Univ, Dept Phys, Tomsk - Russia

• Document type: Journal article
• Source: Journal of Physics A-Mathematical and Theoretical; v. 53, n. 30 JUL 31 2020.
• Web of Science Citations: 0

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 eta-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. (AU)

• FAPESP's process: 16/03319-6 - Non perturbative methods in quantum theory and QFT and their application to actual physical problems
• Grantee: Dmitri Maximovitch Guitman
• Support Opportunities: Research Projects - Thematic Grants