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Title: Aspects of defects in 3d-3d correspondence

Abstract

In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d (2, 0) theory of type AN-1 on a 3-manifold M . The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group SL(N,C) ) on M and a 3d N=2 theory T N [M ]. We study this correspondence in the presence of supersymmetric defects, which are knots/links inside the 3-manifold. Our study employs a number of different methods: state-integral models for complex Chern-Simons theory, cluster algebra techniques, domain wall theory T [SU(N )], 5d N=2 SYM, and also supergravity analysis through holography. These methods are complementary and we find agreement between them. In some cases the results lead to highly non-trivial predictions on the partition function. Our discussion includes a general expression for the cluster partition function, which can be used to compute in the presence of maximal and certain class of non-maximal punctures when N > 2. We also highlight the non-Abelian description of the 3d N=2 T N [M ] theory with defect included, when such a description is available. This paper is a companion to our shorter paper, which summarizes our main results.

Authors:
 [1];  [2];  [3];  [3]
  1. Univ. of Tokyo (Japan)
  2. Kyung Hee Univ., Seoul (Korea); Korea Inst. for Advanced Study, Seoul (Korea)
  3. Inst. for Advanced Study, Princeton, NJ (United States); Univ. of Tokyo (Japan)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1424004
Grant/Contract Number:  
sc0009988
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: 10; 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; M-Theory; Wilson; ’t Hooft and Polyakov loops

Citation Formats

Gang, Dongmin, Kim, Nakwoo, Romo, Mauricio, and Yamazaki, Masahito. Aspects of defects in 3d-3d correspondence. United States: N. p., 2016. Web. doi:10.1007/JHEP10(2016)062.
Gang, Dongmin, Kim, Nakwoo, Romo, Mauricio, & Yamazaki, Masahito. Aspects of defects in 3d-3d correspondence. United States. https://doi.org/10.1007/JHEP10(2016)062
Gang, Dongmin, Kim, Nakwoo, Romo, Mauricio, and Yamazaki, Masahito. Wed . "Aspects of defects in 3d-3d correspondence". United States. https://doi.org/10.1007/JHEP10(2016)062. https://www.osti.gov/servlets/purl/1424004.
@article{osti_1424004,
title = {Aspects of defects in 3d-3d correspondence},
author = {Gang, Dongmin and Kim, Nakwoo and Romo, Mauricio and Yamazaki, Masahito},
abstractNote = {In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d (2, 0) theory of type AN-1 on a 3-manifold M . The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group SL(N,C) ) on M and a 3d N=2 theory T N [M ]. We study this correspondence in the presence of supersymmetric defects, which are knots/links inside the 3-manifold. Our study employs a number of different methods: state-integral models for complex Chern-Simons theory, cluster algebra techniques, domain wall theory T [SU(N )], 5d N=2 SYM, and also supergravity analysis through holography. These methods are complementary and we find agreement between them. In some cases the results lead to highly non-trivial predictions on the partition function. Our discussion includes a general expression for the cluster partition function, which can be used to compute in the presence of maximal and certain class of non-maximal punctures when N > 2. We also highlight the non-Abelian description of the 3d N=2 T N [M ] theory with defect included, when such a description is available. This paper is a companion to our shorter paper, which summarizes our main results.},
doi = {10.1007/JHEP10(2016)062},
journal = {Journal of High Energy Physics (Online)},
number = 10,
volume = 2016,
place = {United States},
year = {2016},
month = {10}
}

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Works referenced in this record:

Boundaries and defects of N = 4 $$ \mathcal{N}=4 $$ SYM with 4 supercharges. Part II: Brane constructions and 3d N = 2 $$ \mathcal{N}=2 $$ field theories
journal, October 2014

  • Hashimoto, Akikazu; Ouyang, Peter; Yamazaki, Masahito
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)108

Wilson loops on three-manifolds and their M2-brane duals
journal, December 2014


N = 2 dualities
journal, August 2012


The superconformal index of the (2,0) theory with defects
journal, May 2015

  • Bullimore, Mathew; Kim, Hee-Cheol
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)048

Boundaries and defects of N = 4 $$ \mathcal{N}=4 $$ SYM with 4 supercharges. Part I: Boundary/junction conditions
journal, October 2014

  • Hashimoto, Akikazu; Ouyang, Peter; Yamazaki, Masahito
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)107

The exact superconformal R-symmetry extremizes Z
journal, May 2012


3d dualities from 4d dualities
journal, July 2013

  • Aharony, Ofer; Razamat, Shlomo S.; Seiberg, Nathan
  • Journal of High Energy Physics, Vol. 2013, Issue 7
  • DOI: 10.1007/JHEP07(2013)149

Exact results for supersymmetric abelian vortex loops in 2 + 1 dimensions
journal, June 2013

  • Kapustin, Anton; Willett, Brian; Yaakov, Itamar
  • Journal of High Energy Physics, Vol. 2013, Issue 6
  • DOI: 10.1007/JHEP06(2013)099

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


Khovanov-Rozansky Homology and Topological Strings
journal, October 2005

  • Gukov, Sergei; Schwarz, Albert; Vafa, Cumrun
  • Letters in Mathematical Physics, Vol. 74, Issue 1
  • DOI: 10.1007/s11005-005-0008-8

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


Spontaneous compactification of seven-dimensional supergravity theories
journal, September 1985


BPS M5-branes as defects for the 3d-3d correspondence
journal, November 2014

  • Bah, Ibrahima; Gabella, Maxime; Halmagyi, Nick
  • Journal of High Energy Physics, Vol. 2014, Issue 11
  • DOI: 10.1007/JHEP11(2014)112

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

  • Kapustin, Anton; Willett, Brian; Yaakov, Itamar
  • Journal of High Energy Physics, Vol. 2010, Issue 3
  • DOI: 10.1007/JHEP03(2010)089

Cluster ensembles, quantization and the dilogarithm
journal, January 2009

  • Fock, Vladimir V.; Goncharov, Alexander B.
  • Annales scientifiques de l'École normale supérieure, Vol. 42, Issue 6
  • DOI: 10.24033/asens.2112

On skein relations in class S theories
journal, June 2015

  • Tachikawa, Yuji; Watanabe, Noriaki
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/JHEP06(2015)186

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


Line operators in theories of class S $$ \mathcal{S} $$ , quantized moduli space of flat connections, and Toda field theory
journal, October 2015

  • Coman, Ioana; Gabella, Maxime; Teschner, Jörg
  • Journal of High Energy Physics, Vol. 2015, Issue 10
  • DOI: 10.1007/JHEP10(2015)143

Wrapped M5-branes, consistent truncations and AdS/CMT
journal, December 2010

  • Donos, Aristomenis; Gauntlett, Jerome P.; Kim, Nakwoo
  • Journal of High Energy Physics, Vol. 2010, Issue 12
  • DOI: 10.1007/JHEP12(2010)003

Holographic Wilson loops
journal, August 2006


Defects and quantum Seiberg-Witten geometry
journal, May 2015

  • Bullimore, Mathew; Kim, Hee-Cheol; Koroteev, Peter
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)095

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


The quantum dilogarithm and representations of quantum cluster varieties
journal, September 2008


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

  • Imamura, Yosuke; Yokoyama, Shuichi
  • Journal of High Energy Physics, Vol. 2011, Issue 4
  • DOI: 10.1007/JHEP04(2011)007

Gauge Theories Labelled by Three-Manifolds
journal, December 2013

  • Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei
  • Communications in Mathematical Physics, Vol. 325, Issue 2
  • DOI: 10.1007/s00220-013-1863-2

Quivers, YBE and 3-manifolds
journal, May 2012


Bipartite field theories: from D-brane probes to scattering amplitudes
journal, November 2012


The complete superconformal index for <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>6</mml:mn></mml:math> Chern–Simons theory
journal, November 2009


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


From necklace quivers to the F -theorem, operator counting, and T (U(N))
journal, December 2011

  • Gulotta, Daniel R.; Herzog, Christopher P.; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2011, Issue 12
  • DOI: 10.1007/JHEP12(2011)077

(1, 1)-knots via the mapping class group of the twice punctured torus
journal, January 2004

  • Cattabriga, Alessia; Mulazzani, Michele
  • Advances in Geometry, Vol. 4, Issue 2
  • DOI: 10.1515/advg.2004.016

Supersymmetric gauge theory, (2,0) theory and twisted 5d Super-Yang-Mills
journal, January 2014


Superconformal index and 3d-3d correspondence for mapping cylinder/torus
journal, January 2014

  • Gang, Dongmin; Koh, Eunkyung; Lee, Sangmin
  • Journal of High Energy Physics, Vol. 2014, Issue 1
  • DOI: 10.1007/JHEP01(2014)063

Notes on SUSY gauge theories on three-sphere
journal, March 2011

  • Hama, Naofumi; Hosomichi, Kazuo; Lee, Sungjay
  • Journal of High Energy Physics, Vol. 2011, Issue 3
  • DOI: 10.1007/JHEP03(2011)127

AGT on the S-duality wall
journal, December 2010

  • Hosomichi, Kazuo; Lee, Sungjay; Park, Jaemo
  • Journal of High Energy Physics, Vol. 2010, Issue 12
  • DOI: 10.1007/JHEP12(2010)079

Framed BPS states
journal, January 2013

  • Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
  • Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 2
  • DOI: 10.4310/ATMP.2013.v17.n2.a1

3d partition function as overlap of wavefunctions
journal, August 2011

  • Nishioka, Tatsuma; Tachikawa, Yuji; Yamazaki, Masahito
  • Journal of High Energy Physics, Vol. 2011, Issue 8
  • DOI: 10.1007/JHEP08(2011)003

Bootstrapping the superconformal index with surface defects
journal, January 2013

  • Gaiotto, Davide; Rastelli, Leonardo; Razamat, Shlomo S.
  • Journal of High Energy Physics, Vol. 2013, Issue 1
  • DOI: 10.1007/JHEP01(2013)022

3D-partition functions on the sphere: exact evaluation and mirror symmetry
journal, May 2012

  • Benvenuti, Sergio; Pasquetti, Sara
  • Journal of High Energy Physics, Vol. 2012, Issue 5
  • DOI: 10.1007/JHEP05(2012)099

The gravity dual of supersymmetric gauge theories on a squashed three-sphere
journal, November 2012


Emergent 3-Manifolds from Four Dimensional Superconformal Indices
journal, August 2012


Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry
journal, January 2010

  • Alday, Luis F.; Gaiotto, Davide; Gukov, Sergei
  • Journal of High Energy Physics, Vol. 2010, Issue 1
  • DOI: 10.1007/JHEP01(2010)113

Webs on surfaces, rings of invariants, and clusters
journal, June 2014

  • Fomin, Sergey; Pylyavskyy, Pavlo
  • Proceedings of the National Academy of Sciences, Vol. 111, Issue 27
  • DOI: 10.1073/pnas.1313068111

Hyperbolicity of partition function and quantum gravity
journal, November 2001


Holography of 3d-3d correspondence at large N
journal, April 2015

  • Gang, Dongmin; Kim, Nakwoo; Lee, Sangmin
  • Journal of High Energy Physics, Vol. 2015, Issue 4
  • DOI: 10.1007/JHEP04(2015)091

The virtue of defects in 4D gauge theories and 2D CFTs
journal, June 2011

  • Drukker, Nadav; Gaiotto, Davide; Gomis, Jaume
  • Journal of High Energy Physics, Vol. 2011, Issue 6
  • DOI: 10.1007/JHEP06(2011)025

New Integrable Models from the Gauge/YBE Correspondence
journal, November 2013


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

  • Hama, Naofumi; Hosomichi, Kazuo; Lee, Sungjay
  • Journal of High Energy Physics, Vol. 2011, Issue 5
  • DOI: 10.1007/JHEP05(2011)014

Dynamics of Script N = 2 supersymmetric Chern-Simons theories
journal, June 2000


The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere
journal, January 2013


Cluster algebras and triangulated surfaces. Part I: Cluster complexes
journal, January 2008


Taming supersymmetric defects in 3d–3d correspondence
journal, June 2016

  • Gang, Dongmin; Kim, Nakwoo; Romo, Mauricio
  • Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 30
  • DOI: 10.1088/1751-8113/49/30/30LT02

Gauge theory loop operators and Liouville theory
journal, February 2010

  • Drukker, Nadav; Gomis, Jaume; Okuda, Takuya
  • Journal of High Energy Physics, Vol. 2010, Issue 2
  • DOI: 10.1007/JHEP02(2010)057

3d-3d correspondence revisited
journal, April 2016

  • Chung, Hee-Joong; Dimofte, Tudor; Gukov, Sergei
  • Journal of High Energy Physics, Vol. 2016, Issue 4
  • DOI: 10.1007/JHEP04(2016)140

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

  • Terashima, Yuji; Yamazaki, Masahito
  • Journal of High Energy Physics, Vol. 2011, Issue 8
  • DOI: 10.1007/JHEP08(2011)135

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

  • Dimofte, Tudor; Gukov, Sergei; Lenells, Jonatan
  • Communications in Number Theory and Physics, Vol. 3, Issue 2
  • DOI: 10.4310/CNTP.2009.v3.n2.a4

Chern-Simons theory and S-duality
journal, May 2013


3-Manifolds and 3d indices
journal, January 2013

  • Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei
  • Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 5
  • DOI: 10.4310/ATMP.2013.v17.n5.a3

Vortex Counting and Lagrangian 3-Manifolds
journal, October 2011

  • Dimofte, Tudor; Gukov, Sergei; Hollands, Lotte
  • Letters in Mathematical Physics, Vol. 98, Issue 3
  • DOI: 10.1007/s11005-011-0531-8

Network and Seiberg duality
journal, September 2012


Electric-magnetic duality in supersymmetric non-Abelian gauge theories
journal, February 1995


The moduli space of vacua of N = 2 $$ \mathcal{N}=2 $$ class S $$ \mathcal{S} $$ theories
journal, October 2014


Wilson Loops in 5d $${\mathcal{N} = 1}$$ SCFTs and AdS/CFT
journal, April 2013


4d quantum geometry from 3d supersymmetric gauge theory and holomorphic block
journal, January 2016


Large N Free Energy of 3d $ \mathcal{N} $ = 4 SCFTs and AdS4/CFT3
journal, September 2012

  • Assel, Benjamin; Estes, John; Yamazaki, Masahito
  • Journal of High Energy Physics, Vol. 2012, Issue 9
  • DOI: 10.1007/JHEP09(2012)074

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

  • Lee, Sungjay; Yamazaki, Masahito
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)035

The gravity duals of $ \mathcal{N}=2 $ superconformal field theories
journal, October 2012

  • Gaiotto, Davide; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)189

Gluing equations for PGL( n, ℂ)–representations of 3–manifolds
journal, January 2015

  • Garoufalidis, Stavros; Goerner, Matthias; Zickert, Christian
  • Algebraic & Geometric Topology, Vol. 15, Issue 1
  • DOI: 10.2140/agt.2015.15.565

Quantum Dilogarithm
journal, February 1994


Holography of wrapped M5-branes and Chern–Simons theory
journal, June 2014


NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d${\mathcal N} = (2, 0)$ THEORIES
journal, February 2013

  • Chacaltana, Oscar; Distler, Jacques; Tachikawa, Yuji
  • International Journal of Modern Physics A, Vol. 28, Issue 03n04
  • DOI: 10.1142/S0217751X1340006X

Wilson loops of anti-symmetric representation and D5-branes
journal, May 2006


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


Quantization of Chern-Simons gauge theory with complex gauge group
journal, March 1991

  • Witten, Edward
  • Communications in Mathematical Physics, Vol. 137, Issue 1
  • DOI: 10.1007/BF02099116

RG domain walls and hybrid triangulations
journal, January 2015

  • Dimofte, Tudor; Gaiotto, Davide; Veen, Roland van der
  • Advances in Theoretical and Mathematical Physics, Vol. 19, Issue 1
  • DOI: 10.4310/ATMP.2015.v19.n1.a2

3d TQFT from 6d SCFT
journal, August 2013


Line operators in theories of class S , quantized moduli space of flat connections, and Toda field theory
text, January 2015

  • Coman, Ioana; Gabella, Maxime; Teschner, Jörg
  • Deutsches Elektronen-Synchrotron, DESY, Hamburg
  • DOI: 10.3204/pubdb-2015-04708

Line operators in theories of class S, quantized moduli space of flat connections, and Toda field theory
text, January 2015

  • Coman, Ioana; Gabella, Maxime; Teschner, Joerg
  • Deutsches Elektronen-Synchrotron, DESY, Hamburg
  • DOI: 10.3204/pubdb-2015-03703

Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group
text, January 2009


Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
text, January 2009


The Virtue of Defects in 4D Gauge Theories and 2D CFTs
text, January 2010


Framed BPS States
preprint, January 2010


Vortex Counting and Lagrangian 3-manifolds
text, January 2010


Notes on SUSY Gauge Theories on Three-Sphere
text, January 2010


SUSY Gauge Theories on Squashed Three-Spheres
text, January 2011


3D-partition functions on the sphere: exact evaluation and mirror symmetry
text, January 2011


From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))
text, January 2011


3d Partition Function as Overlap of Wavefunctions
text, January 2011


The gravity dual of supersymmetric gauge theories on a squashed three-sphere
text, January 2011


3-Manifolds and 3d Indices
preprint, January 2011


Quivers, YBE and 3-manifolds
text, January 2012


Network and Seiberg Duality
text, January 2012


Bootstrapping the superconformal index with surface defects
text, January 2012


Gluing equations for PGL(n,C)-representations of 3-manifolds
text, January 2012


RG Domain Walls and Hybrid Triangulations
preprint, January 2013


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


New Integrable Models from the Gauge/YBE Correspondence
text, January 2013


Holography of Wrapped M5-branes and Chern-Simons theory
text, January 2014


3d-3d Correspondence Revisited
text, January 2014


Holography of 3d-3d correspondence at Large N
text, January 2014


The Superconformal Index of the (2,0) Theory with Defects
text, January 2014


Taming Supersymmetric Defects in 3d-3d Correspondence
text, January 2015


Khovanov-Rozansky Homology and Topological Strings
text, January 2004


(1,1)-knots via the mapping class group of the twice punctured torus
preprint, January 2002


Cluster ensembles, quantization and the dilogarithm
preprint, January 2003


The quantum dilogarithm and representations quantum cluster varieties
text, January 2007


Works referencing / citing this record:

3d dualities from 2d free field correlators: recombination and rank stabilization
journal, January 2020


BPS graphs: from spectral networks to BPS quivers
journal, July 2017

  • Gabella, Maxime; Longhi, Pietro; Park, Chan Y.
  • Journal of High Energy Physics, Vol. 2017, Issue 7
  • DOI: 10.1007/jhep07(2017)032

Symmetry enhancement and closing of knots in 3d/3d correspondence
journal, July 2018


3d N = 2 $$ \mathcal{N}=2 $$ minimal SCFTs from wrapped M5-branes
journal, August 2017

  • Bae, Jin-Beom; Gang, Dongmin; Lee, Jaehoon
  • Journal of High Energy Physics, Vol. 2017, Issue 8
  • DOI: 10.1007/jhep08(2017)118

K-decompositions and 3d gauge theories
journal, November 2016

  • Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B.
  • Journal of High Energy Physics, Vol. 2016, Issue 11
  • DOI: 10.1007/jhep11(2016)151

Equivariant Verlinde Algebra from Superconformal Index and Argyres–Seiberg Duality
journal, January 2018

  • Gukov, Sergei; Pei, Du; Yan, Wenbin
  • Communications in Mathematical Physics, Vol. 357, Issue 3
  • DOI: 10.1007/s00220-017-3074-8

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

Comments on Exchange Graphs in Cluster Algebras
journal, February 2018


Janus and J -fold solutions from Sasaki-Einstein manifolds
journal, October 2019


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


Comments on Exchange Graphs in Cluster Algebras
text, January 2016


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


BPS Graphs: From Spectral Networks to BPS Quivers
text, January 2017


Symmetry enhancement and closing of knots in 3d/3d correspondence
text, January 2018


Janus and J-fold Solutions from Sasaki-Einstein Manifolds
text, January 2019