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4-manifolds and topological modular forms

Gukov, Sergei and Pei, Du and Putrov, Pavel and Vafa, Cumrun (2018) 4-manifolds and topological modular forms. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20191014-080803922

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Abstract

We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1,0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0,1) supersymmetry and, possibly, a residual flavor symmetry. The equivariant topological Witten genus of this 2d theory then produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic (topological) modular forms. We describe basic properties of this map and present a few simple examples. As a byproduct, we obtain some new results on 't Hooft anomalies of 6d (1,0) theories and a better understanding of the relation between 2d (0,1) theories and TMF spectra.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1811.07884arXivDiscussion Paper
ORCID:
AuthorORCID
Pei, Du0000-0001-5587-6905
Additional Information:We would like to thank Ali Daemi, Mike Freedman, Mike Hopkins, Anton Kapustin, Ciprian Manolescu, Kantaro Ohmori, Shlomo Razamat, Peter Teichner, Edward Witten, Ida Zadeh, Gabi Zafrir, and Michele del Zotto for fruitful discussions. We especially would like to thank Peter Teichner for extensive discusions on topological modular forms and Edward Witten for his suggestion to view the 4-manifold invariants we obtain from 6d (1; 0) theories as defining a class in TMF. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of D.P. is supported by the Walter Burke Institute for Theoretical Physics, the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and in part by the center of excellence grant "Center for Quantum Geometry of Moduli Space" from the Danish National Research Foundation (DNRF95). P.P. gratefully acknowledges the support from Marvin L. Goldberger Fellowship and the DOE Grant 51 DE-SC0009988 during his affiliation with IAS. The work of C.V. is supported in part by NSF grant PHY-1067976. We would like to thank the hospitality of Simons Center for Geometry and Physics, Kavli Institute for Theoretical Physics, International Center for Theoretical Physics, and Max Planck Institute for Mathematics where parts of this work were done.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
NSFDMS-1664240
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Danish National Research FoundationDNRF95
Marvin L. Goldberger FellowshipUNSPECIFIED
Department of Energy (DOE)DE-SC0009988
NSFPHY-1067976
Record Number:CaltechAUTHORS:20191014-080803922
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191014-080803922
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99245
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Oct 2019 15:25
Last Modified:14 Oct 2019 15:25

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