APS η-invariant, path integrals, and mock modularity

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 supersymmetr...

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Main Authors:	Atish Dabholkar, Diksha Jain, Arnab Rudra
Format:	Article
Language:	English
Published:	SpringerOpen 2019-11-01
Series:	Journal of High Energy Physics
Subjects:	Anomalies in Field and String Theories Differential and Algebraic Geometry Scattering Amplitudes Sigma Models
Online Access:	http://link.springer.com/article/10.1007/JHEP11(2019)080

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spelling	doaj-71c8fc70d9c043198671b2006ade63c42020-11-25T03:58:35ZengSpringerOpenJournal of High Energy Physics1029-84792019-11-0120191114410.1007/JHEP11(2019)080APS η-invariant, path integrals, and mock modularityAtish Dabholkar0Diksha Jain1Arnab Rudra2Abdus Salam International Centre for Theoretical Physics (ICTP)Abdus Salam International Centre for Theoretical Physics (ICTP)Abdus Salam International Centre for Theoretical Physics (ICTP)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 the noncompact path integral.http://link.springer.com/article/10.1007/JHEP11(2019)080Anomalies in Field and String TheoriesDifferential and Algebraic GeometryScattering AmplitudesSigma Models
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Atish Dabholkar Diksha Jain Arnab Rudra
spellingShingle	Atish Dabholkar Diksha Jain Arnab Rudra APS η-invariant, path integrals, and mock modularity Journal of High Energy Physics Anomalies in Field and String Theories Differential and Algebraic Geometry Scattering Amplitudes Sigma Models
author_facet	Atish Dabholkar Diksha Jain Arnab Rudra
author_sort	Atish Dabholkar
title	APS η-invariant, path integrals, and mock modularity
title_short	APS η-invariant, path integrals, and mock modularity
title_full	APS η-invariant, path integrals, and mock modularity
title_fullStr	APS η-invariant, path integrals, and mock modularity
title_full_unstemmed	APS η-invariant, path integrals, and mock modularity
title_sort	aps η-invariant, path integrals, and mock modularity
publisher	SpringerOpen
series	Journal of High Energy Physics
issn	1029-8479
publishDate	2019-11-01
description	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 the noncompact path integral.
topic	Anomalies in Field and String Theories Differential and Algebraic Geometry Scattering Amplitudes Sigma Models
url	http://link.springer.com/article/10.1007/JHEP11(2019)080
work_keys_str_mv	AT atishdabholkar apsēinvariantpathintegralsandmockmodularity AT dikshajain apsēinvariantpathintegralsandmockmodularity AT arnabrudra apsēinvariantpathintegralsandmockmodularity
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APS η-invariant, path integrals, and mock modularity

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