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APS η-invariant, path integrals, and mock modularity
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DOI：10.1007/JHEP11(2019)080.png)
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Abstract
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We show that the Atiyah-Patodi-Singer eta-invariant can be related to the temperature-dependent Witten index of a noncompact theory and give a new proof of the APS theorem using scattering theory. We relate the eta-invariant to a Callias index and compute it using localization of a supersymmetric path integral. We show that the eta-invariant for the elliptic genus of a finite cigar is related to quantum modular forms obtained from the completion of a mock Jacobi form which we compute from the noncompact path integral.
Keywords:
Anomalies in Field and String Theories
Differential and Algebraic Geometry
Scattering Amplitudes
Sigma Models
Journal
IF:
5.5
Papers:
3.9W
Citations:
13.7W
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