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BPS spectra and 3-manifold invariants

Gukov, Sergei and Pei, Du and Putrov, Pavel and Vafa, Cumrun (2020) BPS spectra and 3-manifold invariants. Journal of Knot Theory and its Ramifications, 29 (2). Art. No. 2040003. ISSN 0218-2165.

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We provide a physical definition of new homological invariants H_a(M₃) of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on M₃ times a 2-disk, D², whose Hilbert space of BPS states plays the role of a basic building block in categorification of various partition functions of 3d N=2 theory T[M₃]: D²×S¹ half-index, S²×S¹ superconformal index, and S²×S¹ topologically twisted index. The first partition function is labeled by a choice of boundary condition and provides a refinement of Chern–Simons (WRT) invariant. A linear combination of them in the unrefined limit gives the analytically continued WRT invariant of M₃. The last two can be factorized into the product of half-indices. We show how this works explicitly for many examples, including Lens spaces, circle fibrations over Riemann surfaces, and plumbed 3-manifolds.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Gukov, Sergei0000-0002-9486-1762
Pei, Du0000-0001-5587-6905
Additional Information:© 2020 World Scientific Publishing Company. Received 7 January 2020; Accepted 13 January 2020; Published 17 March 2020. We would like to thank J. E. Andersen, M. Aganagic, F. Benini, C. Cordova, A.Gadde, E. Gorsky,K. Hori,H. Kim, S. Nawata,M. Romo, S. Shakirov, L. Rozansky and K. Ye for useful comments and discussions. The work of S.G. and D.P. is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. In addition, the work of D.P. is supported 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 DE-SC0009988. The research of C.V. is supported in part by NSF grant PHY-1067976. This work was performed in part (by P.P.) at Aspen Center for Physics which is supported by National Science Foundation grant PHY-1066293. The authors would like to thank Simons Center for Geometry and Physics and the organisers of the Simons Summer Workshop 2016, where the work on the project has begun, for generous hospitality.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Danish National Research FoundationDNRF95
Marvin L. Goldberger FellowshipUNSPECIFIED
Department of Energy (DOE)DE-SC0009988
Subject Keywords:BPS spectrum; 3-manifold; invariant; knot
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Issue or Number:2
Classification Code:AMSC: 57M25, 57M27
Record Number:CaltechAUTHORS:20170201-100930550
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73923
Deposited By: Joy Painter
Deposited On:01 Feb 2017 19:48
Last Modified:14 May 2020 17:39

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