Perturbative fermion anomalies in spacetime dimension d have a well-known relation to Chern-Simons functions in dimension D = d + 1. This relationship is manifested in a beautiful way in “anomaly inflow” from the bulk of a system to its boundary. Along with perturbative anomalies, fermions also have global or nonperturbative anomalies, which can be incorporated by using the η-invariant of Atiyah, Patodi, and Singer instead of the Chern-Simons function. Here we give a nonperturbative description of anomaly inflow, involving the η-invariant. This formula has been expected in the past based on the Dai-Freed theorem, but has not been fully justified. It leads to a general description of perturbative and nonperturbative fermion anomalies in d dimensions in terms of an η-invariant in D dimensions. This η-invariant is a cobordism invariant whenever perturbative anomalies cancel.
|Title of host publication
|Memorial Volume for
|Subtitle of host publication
|World Scientific Publishing Co.
|Number of pages
|Published - Jan 1 2021
All Science Journal Classification (ASJC) codes
- General Engineering
- General Materials Science
- General Physics and Astronomy