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Fivebranes and 3-manifold homology

Gukov, Sergei and Putrov, Pavel and Vafa, Cumrun (2017) Fivebranes and 3-manifold homology. Journal of High Energy Physics, 2017 (07). Art. No. 071. ISSN 1126-6708. doi:10.1007/JHEP07(2017)071.

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Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[M_3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.

Item Type:Article
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URLURL TypeDescription Paper
Gukov, Sergei0000-0002-9486-1762
Additional Information:© 2017 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: 20 October 2016; Revised: 21 April 2017; Accepted: 05 June 2017; First Online: 14 July 2017. Article funded by SCOAP3. We would like to thank M. Aganagic, A. Gadde, M. Khovanov, C. Manolescu, S. Nawata, P. Ozsvath, J. Rasmussen, M. Romo, L. Rozansky, and E. Witten for useful comments and discussions. The work of S.G. is funded in part by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics. P.P. gratefully acknowledges support from the Institute for Advanced Study and also would like to thank Caltech and UT Austin theory groups for hospitality during the final stage of the project. The work of C.V. is supported in part by NSF grant PHY-1067976. C.V. would like to thank KITP for hospitality. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Institute for Advanced StudyUNSPECIFIED
Subject Keywords:Chern-Simons Theories; Topological Field Theories; M-Theory Topological Strings
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Issue or Number:07
Record Number:CaltechAUTHORS:20160316-162103450
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Official Citation:Gukov, S., Putrov, P. & Vafa, C. J. High Energ. Phys. (2017) 2017: 71.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65404
Deposited By: Joy Painter
Deposited On:16 Mar 2016 23:41
Last Modified:10 Nov 2021 23:45

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