Anomaly Inflow and the -Invariant
Sep 18, 2019Citations per year
Abstract: (arXiv)
Perturbative fermion anomalies in spacetime dimension have a well-known relation to Chern-Simons functions in dimension . 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 -invariant of Atiyah, Patodi, and Singer instead of the Chern-Simons function. Here we give a nonperturbative description of anomaly inflow, involving the -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 dimensions in terms of an -invariant in dimensions. This -invariant is a cobordism invariant whenever perturbative anomalies cancel.Note:
- 60 pages. To appear in the proceedings of the Shoucheng Zhang Memorial Workshop. v2: minor improvements and references added. v3: minor corrections
- space-time: dimension
- anomaly
- Chern-Simons term
- nonperturbative
References(62)
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