Anomaly Inflow and the η\eta-Invariant

Sep 18, 2019
60 pages
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Abstract: (arXiv)
Perturbative fermion anomalies in spacetime dimension dd have a well-known relation to Chern-Simons functions in dimension D=d+1D=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\eta-invariant of Atiyah, Patodi, and Singer instead of the Chern-Simons function. Here we give a nonperturbative description of anomaly inflow, involving the η\eta-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 dd dimensions in terms of an η\eta-invariant in DD dimensions. This η\eta-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