Anomaly inflow for local boundary conditions

• Published in: The journal of high energy physics Vol. 2022; no. 9; pp. 250 - 20
• Main Authors: Ivanov, A. V., Vassilevich, D. V.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 30-09-2022; Springer Nature B.V; SpringerOpen
• Subjects: Anomalies in Field and String Theories; Boundary conditions; Boundary Quantum Field Theory; Boundary value problems; Classical and Quantum Gravitation; Eigenvalues; Elementary Particles; Ellipticity; High energy physics; Invariants; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Boundary Quantum Field Theory; Anomalies in Field and String Theories
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2022)250

A
bstract
We study the
η
-invariant of a Dirac operator on a manifold with boundary subject to local boundary conditions with the help of heat kernel methods. In even dimensions, we relate this invariant to
η
-invariants of a boundary Dirac operator, while in odd dimension, it is expressed through the index of boundary operators. We stress the necessity of the strong ellipticity condition for the applicability of our methods. We show that the Witten-Yonekura boundary conditions are not strongly elliptic, though they are very close to strongly elliptic ones.