3d-3d correspondence revisited

Chung, Hee -Joong; Dimofte, Tudor; Gukov, Sergei; Sułkowski, Piotr

doi:10.1007/JHEP04(2016)140

Title: 3d-3d correspondence revisited

Abstract

In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N = 2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. As a result, we also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.

Authors:

Chung, Hee -Joong ^[1]; Dimofte, Tudor ^[2]; Gukov, Sergei ^[3]; Sułkowski, Piotr ^[4]

California Inst. of Technology (CalTech), Pasadena, CA (United States)
Institute for Advanced Study, Princeton, NJ (United States)
California Inst. of Technology (CalTech), Pasadena, CA (United States); Max-Planck-Institut fur Mathematik, Bonn (Germany)
California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of Warsaw, Warsaw (Poland)

Publication Date:: Thu Apr 21 00:00:00 EDT 2016

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1326969

Grant/Contract Number:: FG02-92ER40701; SC0011632

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 4; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; supersymmetric gauge theory; topological field theories; Chern-Simons theories; supersymmetry and duality

Citation Formats


                    Chung, Hee -Joong, Dimofte, Tudor, Gukov, Sergei, and Sułkowski, Piotr. 3d-3d correspondence revisited.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP04(2016)140.

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                    Chung, Hee -Joong, Dimofte, Tudor, Gukov, Sergei, & Sułkowski, Piotr. 3d-3d correspondence revisited.  United States.  https://doi.org/10.1007/JHEP04(2016)140

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                    Chung, Hee -Joong, Dimofte, Tudor, Gukov, Sergei, and Sułkowski, Piotr. Thu .  
"3d-3d correspondence revisited".  United States.  https://doi.org/10.1007/JHEP04(2016)140.  https://www.osti.gov/servlets/purl/1326969.

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@article{osti_1326969,

  title        = {3d-3d correspondence revisited},

  author       = {Chung, Hee -Joong and Dimofte, Tudor and Gukov, Sergei and Sułkowski, Piotr},

  abstractNote = {In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N = 2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. As a result, we also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.},

  doi          = {10.1007/JHEP04(2016)140},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 4,

  volume       = 2016,

  place        = {United States},

  year         = {Thu Apr 21 00:00:00 EDT 2016},

  month        = {Thu Apr 21 00:00:00 EDT 2016}

}

Copy to clipboard

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Beem, Christopher; Dimofte, Tudor; Pasquetti, Sara
arXiv
DOI: 10.48550/arxiv.1211.1986

Tangles, Generalized Reidemeister Moves, and Three-Dimensional Mirror Symmetry
preprint, January 2012

Cordova, Clay; Espahbodi, Sam; Haghighat, Babak
arXiv
DOI: 10.48550/arxiv.1211.3730

RG Domain Walls and Hybrid Triangulations
preprint, January 2013

Dimofte, Tudor; Gaiotto, Davide; van der Veen, Roland
arXiv
DOI: 10.48550/arxiv.1304.6721

3d Chern-Simons Theory from M5-branes
text, January 2013

Lee, Sungjay; Yamazaki, Masahito
arXiv
DOI: 10.48550/arxiv.1305.2429

Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit
text, January 2013

Kokenyesi, Zoltan; Sinkovics, Annamaria; Szabo, Richard J.
arXiv
DOI: 10.48550/arxiv.1306.1707

Chern-Simons Theory on Seifert 3-Manifolds
text, January 2013

Blau, Matthias; Thompson, George
arXiv
DOI: 10.48550/arxiv.1306.3381

Complex Chern-Simons theory at level k via the 3d-3d correspondence
preprint, January 2014

Dimofte, Tudor
arXiv
DOI: 10.48550/arxiv.1409.0857

Knots, links and branes at large N
text, January 2000

Labastida, J. M. F.; Marino, Marcos; Vafa, Cumrun
arXiv
DOI: 10.48550/arxiv.hep-th/0010102

Matrix Models, Geometric Engineering and Elliptic Genera
text, January 2003

Hollowood, Timothy J.; Iqbal, Amer; Vafa, Cumrun
arXiv
DOI: 10.48550/arxiv.hep-th/0310272

Khovanov-Rozansky Homology and Topological Strings
text, January 2004

Gukov, Sergei; Schwarz, Albert; Vafa, Cumrun
arXiv
DOI: 10.48550/arxiv.hep-th/0412243

Discrete and oscillatory Matrix Models in Chern-Simons theory
text, January 2005

de Haro, Sebastian; Tierz, Miguel
arXiv
DOI: 10.48550/arxiv.hep-th/0501123

Non-Abelian Localization For Chern-Simons Theory
text, January 2005

Beasley, Chris; Witten, Edward
arXiv
DOI: 10.48550/arxiv.hep-th/0503126

Phases of $N=2$ Theories In Two Dimensions
text, January 1993

Witten, Edward
arXiv
DOI: 10.48550/arxiv.hep-th/9301042

A Strong Coupling Test of S-Duality
text, January 1994

Vafa, Cumrun; Witten, Edward
arXiv
DOI: 10.48550/arxiv.hep-th/9408074

Mirror Symmetry in Three Dimensional Gauge Theories
text, January 1996

Intriligator, K.; Seiberg, N.
arXiv
DOI: 10.48550/arxiv.hep-th/9607207

D-branes, Monopoles and Nahm Equations
text, January 1996

Diaconescu, Duiliu-Emanuel
arXiv
DOI: 10.48550/arxiv.hep-th/9608163

Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
text, January 1997

Aharony, O.; Hanany, A.; Intriligator, K.
arXiv
DOI: 10.48550/arxiv.hep-th/9703110

Solutions Of Four-Dimensional Field Theories Via M Theory
text, January 1997

Witten, Edward
arXiv
DOI: 10.48550/arxiv.hep-th/9703166

Euclidean SYM Theories by Time Reduction and Special Holonomy Manifolds
text, January 1997

Blau, Matthias; Thompson, George
arXiv
DOI: 10.48550/arxiv.hep-th/9706225

Framed knot contact homology
text, January 2004

Ng, Lenhard
arXiv
DOI: 10.48550/arxiv.math/0407071

Works referencing / citing this record:

All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern–Simons Theory
journal, March 2018

Gang, Dongmin; Romo, Mauricio; Yamazaki, Masahito
Communications in Mathematical Physics, Vol. 359, Issue 3
DOI: 10.1007/s00220-018-3115-y

K-Decompositions and 3d Gauge Theories
preprint, January 2013

Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B.
arXiv
DOI: 10.48550/arxiv.1301.0192

Aspects of Defects in 3d-3d Correspondence
text, January 2015

Gang, Dongmin; Kim, Nakwoo; Romo, Mauricio
arXiv
DOI: 10.48550/arxiv.1510.05011

All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory
text, January 2017

Gang, Dongmin; Romo, Mauricio; Yamazaki, Masahito
arXiv
DOI: 10.48550/arxiv.1704.00918

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Title: 3d-3d correspondence revisited

Abstract

Citation Formats

Vortex Counting and Lagrangian 3-Manifolds journal, October 2011

Gauge Theories Labelled by Three-Manifolds journal, December 2013

Bootstrapping the superconformal index with surface defects journal, January 2013

The superconformal index and an elliptic algebra of surface defects journal, October 2014

Down the rabbit hole with theories of class S $$ \mathcal{S} $$ journal, October 2014

Walls, lines, and spectral dualities in 3d gauge theories journal, May 2014

A categorification of the Jones polynomial journal, February 2000

Quantum ( sl n , ∧V n ) link invariant and matrix factorizations journal, December 2011

Quantum field theory and the Jones polynomial journal, September 1989

A new polynomial invariant of knots and links journal, April 1985

Super-A-polynomial for knots and BPS states journal, February 2013

Superpolynomials for torus knots from evolution induced by cut-and-join operators journal, March 2013

Knot Homology and Refined Chern–Simons Index journal, November 2014

Volume conjecture: refined and categorified journal, January 2012

Link Homologies and the Refined Topological Vertex journal, April 2010

HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations journal, July 2012

Super-A-polynomials for twist knots journal, November 2012

Chern-Simons Theory, Matrix Integrals, and Perturbative Three-Manifold Invariants journal, November 2004

Non-Abelian localization for Chern-Simons theory journal, June 2005

A note on knot invariants and q -deformed 2d Yang–Mills journal, March 2006

Chern-Simons theory on Seifert 3-manifolds journal, September 2013

Exact results for Wilson loops in superconformal Chern-Simons theories with matter journal, March 2010

SUSY gauge theories on squashed three-spheres journal, May 2011

Index for three dimensional superconformal field theories with general R-charge assignments journal, April 2011

Plane curves associated to character varieties of 3-manifolds journal, December 1994

Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial journal, March 2005

Quantum Riemann surfaces in Chern-Simons theory journal, January 2013

A-polynomial, B-model, and quantization journal, February 2012

On the characteristic and deformation varieties of a knot conference, September 2004

Framed knot contact homology journal, February 2008

Combinatorial knot contact homology and transverse knots journal, August 2011

Analytic continuation of Chern-Simons theory book, January 2010

$ {\text{SL}}\left( {2,\mathbb{R}} \right) $ Chern-Simons, Liouville, and gauge theory on duality walls journal, August 2011

Tangles, generalized Reidemeister moves, and three-dimensional mirror symmetry journal, May 2014

Aspects of N = 2 supersymmetric gauge theories in three dimensions journal, August 1997

Mirror symmetry in three dimensional gauge theories journal, October 1996

Mirror symmetry in three-dimensional gauge theories, and D-brane moduli spaces journal, May 1997

Phases of N = 2 theories in two dimensions journal, August 1993

Supersymmetric Vacua and Bethe Ansatz journal, July 2009

Knot invariants from four-dimensional gauge theory journal, January 2012

RG domain walls and hybrid triangulations journal, January 2015

Supersymmetric Boundary Conditions in $\mathcal{N}=4$ Super Yang-Mills Theory journal, February 2009

Gauge theory and knot homologies journal, May 2007

A strong coupling test of S-duality journal, December 1994

Supersymmetric gauge theories, intersecting branes and free fermions journal, February 2008

Instantons on ALE spaces and orbifold partitions journal, March 2008

Matrix model as a mirror of Chern-Simons theory journal, February 2004

Witten-Reshetikhin-Turaev Invariants of�Seifert Manifolds journal, August 1999

Discrete and oscillatory matrix models in Chern–Simons theory journal, December 2005

Seiberg–Witten theory and matrix models journal, October 2009

A Matrix Model for the Topological String I: Deriving the Matrix Model journal, December 2013

Wall Crossing as Seen by Matrix Models journal, September 2011

q-deformations of two-dimensional Yang–Mills theory: Classification, categorification and refinement journal, November 2013

Refined Chern-Simons theory and (q, t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit journal, October 2013

Introduction book, January 1983

Solutions of four-dimensional field theories via M-theory journal, September 1997

Knot invariants and topological strings journal, June 2000

Knots, links and branes at large N journal, November 2000

Seiberg-Witten Prepotential from Instanton Counting journal, January 2003

Matrix models, geometric engineering and elliptic genera journal, March 2008

Khovanov-Rozansky Homology and Topological Strings journal, October 2005

Large N Duality, Lagrangian Cycles, and Algebraic Knots journal, October 2012

Topological strings, D-model, and knot contact homology journal, January 2014

Aspects of NT ⩾ 2 topological gauge theories and D-branes journal, May 1997

Euclidean SYM theories by time reduction and special holonomy manifolds journal, December 1997

D-branes and topological field theories journal, March 1996

A Hyper-KÄHlerian Structure on Coadjoint Orbits of a Semisimple Complex Group journal, October 1990

Instantons and the geometry of the nilpotent variety journal, January 1990

$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory journal, January 2009

3d Chern-Simons theory from M5-branes journal, December 2013

3d TQFT from 6d SCFT journal, August 2013

Complex Chern–Simons Theory at Level k via the 3d–3d Correspondence journal, June 2015

A TQFT from Quantum Teichmüller Theory journal, June 2014

Generalized volume conjecture and the A -polynomials: The Neumann–Zagier potential function as a classical limit of the partition function journal, August 2007

Exact results for perturbative Chern–Simons theory with complex gauge group journal, January 2009

Homological algebra of knots and BPS states conference, May 2013

Quantum (sln, ∧V n ) link invariant and matrix factorizations journal, December 2011

Vortex Counting and Lagrangian 3-Manifolds
journal, October 2011

Gauge Theories Labelled by Three-Manifolds
journal, December 2013

Bootstrapping the superconformal index with surface defects
journal, January 2013

The superconformal index and an elliptic algebra of surface defects
journal, October 2014

Down the rabbit hole with theories of class S $$ \mathcal{S} $$
journal, October 2014

Walls, lines, and spectral dualities in 3d gauge theories
journal, May 2014

A categorification of the Jones polynomial
journal, February 2000

Quantum ( sl _n , ∧V _n ) link invariant and matrix factorizations
journal, December 2011

Quantum field theory and the Jones polynomial
journal, September 1989

A new polynomial invariant of knots and links
journal, April 1985

Super-A-polynomial for knots and BPS states
journal, February 2013

Superpolynomials for torus knots from evolution induced by cut-and-join operators
journal, March 2013

Knot Homology and Refined Chern–Simons Index
journal, November 2014

Volume conjecture: refined and categorified
journal, January 2012

Link Homologies and the Refined Topological Vertex
journal, April 2010

HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
journal, July 2012

Super-A-polynomials for twist knots
journal, November 2012

Chern-Simons Theory, Matrix Integrals, and Perturbative Three-Manifold Invariants
journal, November 2004

Non-Abelian localization for Chern-Simons theory
journal, June 2005

A note on knot invariants and q -deformed 2d Yang–Mills
journal, March 2006

Chern-Simons theory on Seifert 3-manifolds
journal, September 2013

Exact results for Wilson loops in superconformal Chern-Simons theories with matter
journal, March 2010

SUSY gauge theories on squashed three-spheres
journal, May 2011

Index for three dimensional superconformal field theories with general R-charge assignments
journal, April 2011

Plane curves associated to character varieties of 3-manifolds
journal, December 1994

Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
journal, March 2005

Quantum Riemann surfaces in Chern-Simons theory
journal, January 2013

A-polynomial, B-model, and quantization
journal, February 2012

On the characteristic and deformation varieties of a knot
conference, September 2004

Framed knot contact homology
journal, February 2008

Combinatorial knot contact homology and transverse knots
journal, August 2011

Analytic continuation of Chern-Simons theory
book, January 2010

$ {\text{SL}}\left( {2,\mathbb{R}} \right) $ Chern-Simons, Liouville, and gauge theory on duality walls
journal, August 2011

Tangles, generalized Reidemeister moves, and three-dimensional mirror symmetry
journal, May 2014

Aspects of N = 2 supersymmetric gauge theories in three dimensions
journal, August 1997

Mirror symmetry in three dimensional gauge theories
journal, October 1996

Mirror symmetry in three-dimensional gauge theories, and D-brane moduli spaces
journal, May 1997

Phases of N = 2 theories in two dimensions
journal, August 1993

Supersymmetric Vacua and Bethe Ansatz
journal, July 2009

Knot invariants from four-dimensional gauge theory
journal, January 2012

RG domain walls and hybrid triangulations
journal, January 2015

Supersymmetric Boundary Conditions in $\mathcal{N}=4$ Super Yang-Mills Theory
journal, February 2009

Gauge theory and knot homologies
journal, May 2007

A strong coupling test of S-duality
journal, December 1994

Supersymmetric gauge theories, intersecting branes and free fermions
journal, February 2008

Instantons on ALE spaces and orbifold partitions
journal, March 2008

Matrix model as a mirror of Chern-Simons theory
journal, February 2004

Witten-Reshetikhin-Turaev Invariants of�Seifert Manifolds
journal, August 1999

Discrete and oscillatory matrix models in Chern–Simons theory
journal, December 2005

Seiberg–Witten theory and matrix models
journal, October 2009

A Matrix Model for the Topological String I: Deriving the Matrix Model
journal, December 2013

Wall Crossing as Seen by Matrix Models
journal, September 2011

q-deformations of two-dimensional Yang–Mills theory: Classification, categorification and refinement
journal, November 2013

Refined Chern-Simons theory and (q, t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit
journal, October 2013

Introduction
book, January 1983

Solutions of four-dimensional field theories via M-theory
journal, September 1997

Knot invariants and topological strings
journal, June 2000

Knots, links and branes at large N
journal, November 2000

Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003

Matrix models, geometric engineering and elliptic genera
journal, March 2008

Khovanov-Rozansky Homology and Topological Strings
journal, October 2005

Large N Duality, Lagrangian Cycles, and Algebraic Knots
journal, October 2012

Topological strings, D-model, and knot contact homology
journal, January 2014

Aspects of NT ⩾ 2 topological gauge theories and D-branes
journal, May 1997

Euclidean SYM theories by time reduction and special holonomy manifolds
journal, December 1997

D-branes and topological field theories
journal, March 1996

A Hyper-KÄHlerian Structure on Coadjoint Orbits of a Semisimple Complex Group
journal, October 1990

Instantons and the geometry of the nilpotent variety
journal, January 1990

$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory
journal, January 2009

3d Chern-Simons theory from M5-branes
journal, December 2013

3d TQFT from 6d SCFT
journal, August 2013

Complex Chern–Simons Theory at Level k via the 3d–3d Correspondence
journal, June 2015

A TQFT from Quantum Teichmüller Theory
journal, June 2014

Generalized volume conjecture and the $A$ -polynomials: The Neumann–Zagier potential function as a classical limit of the partition function
journal, August 2007

Exact results for perturbative Chern–Simons theory with complex gauge group
journal, January 2009

Homological algebra of knots and BPS states
conference, May 2013

Quantum (sln, ∧V n ) link invariant and matrix factorizations
journal, December 2011

Discrete and oscillatory matrix models in Chern-Simons theory
text, January 2005

A note on knot invariants and q-deformed 2d Yang-Mills
text, January 2006

Link Homologies and the Refined Topological Vertex
text, January 2007