Anomaly Inflow and the η-Invariant

Edward Witten, Kazuya Yonekura

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

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 languageEnglish (US)
Title of host publicationMemorial Volume for
Subtitle of host publicationShoucheng Zhang
PublisherWorld Scientific Publishing Co.
Pages283-352
Number of pages70
ISBN (Electronic)9789811231711
ISBN (Print)9789811231704
DOIs
StatePublished - Jan 1 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Materials Science(all)
  • Physics and Astronomy(all)

Fingerprint

Dive into the research topics of 'Anomaly Inflow and the η-Invariant'. Together they form a unique fingerprint.

Cite this