Abstract
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.
Original language | English (US) |
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Title of host publication | Memorial Volume for |
Subtitle of host publication | Shoucheng Zhang |
Publisher | World Scientific Publishing Co. |
Pages | 283-352 |
Number of pages | 70 |
ISBN (Electronic) | 9789811231711 |
ISBN (Print) | 9789811231704 |
DOIs | |
State | Published - Jan 1 2021 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Engineering
- General Materials Science
- General Physics and Astronomy