Abstract
We show that the Atiyah-Patodi-Singer η-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 η-invariant to a Callias index and compute it using localization of a supersymmetric path integral. We show that the η-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.
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Dedicated to the memory of Michael Atiyah
ArXiv ePrint: 1905.05207
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Dabholkar, A., Jain, D. & Rudra, A. APS η-invariant, path integrals, and mock modularity. J. High Energ. Phys. 2019, 80 (2019). https://doi.org/10.1007/JHEP11(2019)080
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DOI: https://doi.org/10.1007/JHEP11(2019)080