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.
APS η-invariant, path integrals, and mock modularity / Dabholkar, Atish; Jain, Diksha; Rudra, Arnab. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2019:11(2019), pp. 1-44. [10.1007/jhep11(2019)080]
APS η-invariant, path integrals, and mock modularity
Jain, Diksha;
2019-01-01
Abstract
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.| File | Dimensione | Formato | |
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