Fivebranes and 3manifold homology
Abstract
Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3manifolds. We show that vebrane compacti cations provide a universal description of various old and new homological invariants of 3manifolds. In terms of 3d/3d correspondence, such invariants are given by the Qcohomology 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 3manifold analog of KhovanovRozansky link homology. The latter gives a categori cation of ChernSimons partition function. Finally, some of the new key elements include the explicit form of the Stransform and a novel connection between categori cation and a previously mysterious role of Eichler integrals in ChernSimons theory.
 Authors:
 California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
 School of Natural Sciences, Inst.for Advanced Study, Princeton, NJ (United States)
 Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab.
 Publication Date:
 Research Org.:
 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org.:
 USDOE; National Science Foundation (NSF)
 OSTI Identifier:
 1393398
 Grant/Contract Number:
 SC0011632; PHY1067976
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 7; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ChernSimons Theories; Topological Field Theories; MTheory; Topological Strings
Citation Formats
Gukov, Sergei, Putrov, Pavel, and Vafa, Cumrun. Fivebranes and 3manifold homology. United States: N. p., 2017.
Web. doi:10.1007/JHEP07(2017)071.
Gukov, Sergei, Putrov, Pavel, & Vafa, Cumrun. Fivebranes and 3manifold homology. United States. doi:10.1007/JHEP07(2017)071.
Gukov, Sergei, Putrov, Pavel, and Vafa, Cumrun. 2017.
"Fivebranes and 3manifold homology". United States.
doi:10.1007/JHEP07(2017)071. https://www.osti.gov/servlets/purl/1393398.
@article{osti_1393398,
title = {Fivebranes and 3manifold homology},
author = {Gukov, Sergei and Putrov, Pavel and Vafa, Cumrun},
abstractNote = {Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3manifolds. We show that vebrane compacti cations provide a universal description of various old and new homological invariants of 3manifolds. In terms of 3d/3d correspondence, such invariants are given by the Qcohomology of the Hilbert space of partially topologically twisted 3d N = 2 theory T[M3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3manifold analog of KhovanovRozansky link homology. The latter gives a categori cation of ChernSimons partition function. Finally, some of the new key elements include the explicit form of the Stransform and a novel connection between categori cation and a previously mysterious role of Eichler integrals in ChernSimons theory.},
doi = {10.1007/JHEP07(2017)071},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2017,
place = {United States},
year = 2017,
month = 7
}
Web of Science

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