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Title: Fivebranes and 3-manifold homology

Abstract

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that vebrane compacti cations 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 categori cation of Chern-Simons partition function. Finally, some of the new key elements include the explicit form of the S-transform and a novel connection between categori cation and a previously mysterious role of Eichler integrals in Chern-Simons theory.

Authors:
 [1];  [2];  [3]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
  2. School of Natural Sciences, Inst.for Advanced Study, Princeton, NJ (United States)
  3. 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; PHY-1067976
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 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Chern-Simons Theories; Topological Field Theories; M-Theory; Topological Strings

Citation Formats

Gukov, Sergei, Putrov, Pavel, and Vafa, Cumrun. Fivebranes and 3-manifold homology. United States: N. p., 2017. Web. doi:10.1007/JHEP07(2017)071.
Gukov, Sergei, Putrov, Pavel, & Vafa, Cumrun. Fivebranes and 3-manifold homology. United States. doi:10.1007/JHEP07(2017)071.
Gukov, Sergei, Putrov, Pavel, and Vafa, Cumrun. Fri . "Fivebranes and 3-manifold homology". United States. doi:10.1007/JHEP07(2017)071. https://www.osti.gov/servlets/purl/1393398.
@article{osti_1393398,
title = {Fivebranes and 3-manifold 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 3-manifolds. We show that vebrane compacti cations 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[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 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categori cation of Chern-Simons partition function. Finally, some of the new key elements include the explicit form of the S-transform and a novel connection between categori cation and a previously mysterious role of Eichler integrals in Chern-Simons theory.},
doi = {10.1007/JHEP07(2017)071},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2017,
place = {United States},
year = {Fri Jul 14 00:00:00 EDT 2017},
month = {Fri Jul 14 00:00:00 EDT 2017}
}

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Cited by: 7 works
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