# APS η-invariant, path integrals, and mock modularity

@article{Dabholkar2019APSP, title={APS $\eta$-invariant, path integrals, and mock modularity}, author={Atish Dabholkar and Diksha Jain and Arnab Rudra}, journal={Journal of High Energy Physics}, year={2019} }

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…

## 10 Citations

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Abstract
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Perturbative fermion anomalies in spacetime dimension $d$ have a well-known relation to Chern-Simons functions in dimension $D=d+1$. This relationship is manifested in a beautiful way in "anomaly…

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