Anomaly Inflow and the η-Invariant

Edward Witten, Kazuya Yonekura

Research output: Contribution to journalArticlepeer-review


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. (To be submitted to the proceedings of the Shoucheng Zhang Memorial Workshop.)

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Sep 18

ASJC Scopus subject areas

  • General

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