APS $\eta$-invariant, path integrals, and mock modularity
| Autor: | Dabholkar, Atish, Jain, Diksha, Rudra, Arnab |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP11(2019)080 |
| Popis: | 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. Comment: 44 pages, 5 figues |
| Databáze: | arXiv |
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