APS η-invariant, path integrals, and mock modularity

  title={APS $\eta$-invariant, path integrals, and mock modularity},
  author={Atish Dabholkar and Diksha Jain and Arnab Rudra},
  journal={Journal of High Energy Physics},
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… 

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