APS ηinvariant, path integrals, and mock modularity
Abstract
We show that the AtiyahPatodiSinger ηinvariant can be related to the temperaturedependent Witten index of a noncompact theory and give a new proof of the APS theorem using scattering theory. We relate the ηinvariant to a Callias index and compute it using localization of a supersymmetric path integral. We show that the ηinvariant 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 November 2019
 DOI:
 10.1007/JHEP11(2019)080
 arXiv:
 arXiv:1905.05207
 Bibcode:
 2019JHEP...11..080D
 Keywords:

 Anomalies in Field and String Theories;
 Differential and Algebraic Geometry;
 Scattering Amplitudes;
 Sigma Models;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 44 pages, 5 figues