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Article Dans Une Revue Journal of High Energy Physics Année : 2019

APS $\eta$-invariant, path integrals, and mock modularity

Résumé

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.

Dates et versions

hal-02147943 , version 1 (05-06-2019)

Identifiants

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Atish Dabholkar, Diksha Jain, Arnab Rudra. APS $\eta$-invariant, path integrals, and mock modularity. Journal of High Energy Physics, 2019, 11, pp.080. ⟨10.1007/JHEP11(2019)080⟩. ⟨hal-02147943⟩
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