Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory
Abstract
We introduce several families of N = (2, 2) UV boundary conditions in 3d N=4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality $$-$$ an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.
- Authors:
-
- Univ. of Oxford (United Kingdom). Mathematical Inst.; Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
- Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics, Dept. of Mathematics
- Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
- Univ. of Oregon, Eugene, OR (United States). Dept. of Mathematics
- Publication Date:
- Research Org.:
- Univ. of Oxford (United Kingdom)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); European Research Council (ERC)
- OSTI Identifier:
- 1358546
- Grant/Contract Number:
- SC0009988; 335739; 306260
- 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; Supersymmetric Gauge Theory; Supersymmetry and Duality; Topological Field Theories; Solitons Monopoles and Instantons
Citation Formats
Bullimore, Mathew, Dimofte, Tudor, Gaiotto, Davide, and Hilburn, Justin. Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory. United States: N. p., 2016.
Web. doi:10.1007/JHEP10(2016)108.
Bullimore, Mathew, Dimofte, Tudor, Gaiotto, Davide, & Hilburn, Justin. Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory. United States. https://doi.org/10.1007/JHEP10(2016)108
Bullimore, Mathew, Dimofte, Tudor, Gaiotto, Davide, and Hilburn, Justin. Thu .
"Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory". United States. https://doi.org/10.1007/JHEP10(2016)108. https://www.osti.gov/servlets/purl/1358546.
@article{osti_1358546,
title = {Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory},
author = {Bullimore, Mathew and Dimofte, Tudor and Gaiotto, Davide and Hilburn, Justin},
abstractNote = {We introduce several families of N = (2, 2) UV boundary conditions in 3d N=4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality $-$ an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.},
doi = {10.1007/JHEP10(2016)108},
journal = {Journal of High Energy Physics (Online)},
number = 10,
volume = 2016,
place = {United States},
year = {Thu Oct 20 00:00:00 EDT 2016},
month = {Thu Oct 20 00:00:00 EDT 2016}
}
Web of Science
Works referenced in this record:
Hyperkähler metrics and supersymmetry
journal, December 1987
- Hitchin, N. J.; Karlhede, A.; Lindström, U.
- Communications in Mathematical Physics, Vol. 108, Issue 4
Three-dimensional topological field theory and symplectic algebraic geometry I
journal, August 2009
- Kapustin, Anton; Rozansky, Lev; Saulina, Natalia
- Nuclear Physics B, Vol. 816, Issue 3
Three-dimensional topological field theory and symplectic algebraic geometry II
journal, January 2010
- Kapustin, Anton; Rozansky, Lev
- Communications in Number Theory and Physics, Vol. 4, Issue 3
Ω-deformation and quantization
journal, August 2014
- Yagi, Junya
- Journal of High Energy Physics, Vol. 2014, Issue 8
The geometry and topology of toric hyperkähler manifolds
journal, January 2000
- Bielawski, Roger; Dancer, Andrew S.
- Communications in Analysis and Geometry, Vol. 8, Issue 4
Toric Topology
book, January 2008
- Harada, Megumi; Karshon, YAel; Masuda, Mikiya
- Contemporary Mathematics, Vol. 460
Mirror symmetry in three dimensional gauge theories
journal, October 1996
- Intriligator, K.; Seiberg, N.
- Physics Letters B, Vol. 387, Issue 3
Gauge Theories Labelled by Three-Manifolds
journal, December 2013
- Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei
- Communications in Mathematical Physics, Vol. 325, Issue 2
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
Supersymmetric Boundary Conditions in $\mathcal{N}=4$ Super Yang-Mills Theory
journal, February 2009
- Gaiotto, Davide; Witten, Edward
- Journal of Statistical Physics, Vol. 135, Issue 5-6
$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory
journal, January 2009
- Gaiotto, David; Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 13, Issue 3
D -Particle Bound States and Generalized Instantons
journal, January 2000
- Moore, Gregory; Nekrasov, Nikita; Shatashvili, Samson
- Communications in Mathematical Physics, Vol. 209, Issue 1
Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003
- Nekrasov, Nikita A.
- Advances in Theoretical and Mathematical Physics, Vol. 7, Issue 5
Quantization of Integrable Systems and four Dimensional Gauge Theories
conference, January 2012
- Nekrasov, Nikita A.; Shatashvili, Samson L.
- XVIth International Congress on Mathematical Physics
Refined, Motivic, and Quantum
journal, November 2009
- Dimofte, Tudor; Gukov, Sergei
- Letters in Mathematical Physics, Vol. 91, Issue 1
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
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
The omega deformation, branes, integrability and Liouville theory
journal, September 2010
- Nekrasov, Nikita; Witten, Edward
- Journal of High Energy Physics, Vol. 2010, Issue 9
Quantization of the Hitchin moduli spaces, Liouville theory and the geometric Langlands correspondence I
journal, January 2011
- Teschner, J.
- Advances in Theoretical and Mathematical Physics, Vol. 15, Issue 2
Framed BPS states
journal, January 2013
- Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
- Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 2
D-branes and topological field theories
journal, March 1996
- Bershadsky, M.; Vafa, C.; Sadov, V.
- Nuclear Physics B, Vol. 463, Issue 2-3
Electric-magnetic duality and the geometric Langlands program
journal, January 2007
- Kapustin, Anton; Witten, Edward
- Communications in Number Theory and Physics, Vol. 1, Issue 1
N = 2 dualities
journal, August 2012
- Gaiotto, Davide
- Journal of High Energy Physics, Vol. 2012, Issue 8
Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
journal, July 2010
- Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
- Communications in Mathematical Physics, Vol. 299, Issue 1
Five dimensional SUSY field theories, non-trivial fixed points and string dynamics
journal, November 1996
- Seiberg, Nathan
- Physics Letters B, Vol. 388, Issue 4
Extremal transitions and five-dimensional supersymmetric field theories
journal, January 1997
- Morrison, David R.; Seiberg, Nathan
- Nuclear Physics B, Vol. 483, Issue 1-2
Small instantons, del Pezzo surfaces and type I' theory
journal, July 1997
- Douglas, Michael R.; Katz, Sheldon; Vafa, Cumrun
- Nuclear Physics B, Vol. 497, Issue 1-2
Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces
journal, July 1997
- Intriligator, Kenneth; Morrison, David R.; Seiberg, Nathan
- Nuclear Physics B, Vol. 497, Issue 1-2
Branes, superpotentials and superconformal fixed points
journal, October 1997
- Aharony, Ofer; Hanany, Amihay
- Nuclear Physics B, Vol. 504, Issue 1-2
Hyper-Kähler geometry and invariants of three-manifolds
journal, September 1997
- Rozansky, L.; Witten, E.
- Selecta Mathematica, Vol. 3, Issue 3
Aspects of NT ⩾ 2 topological gauge theories and D-branes
journal, May 1997
- Blau, Matthias; Thompson, George
- Nuclear Physics B, Vol. 492, Issue 3
Walls, lines, and spectral dualities in 3d gauge theories
journal, May 2014
- Gadde, Abhijit; Gukov, Sergei; Putrov, Pavel
- Journal of High Energy Physics, Vol. 2014, Issue 5
Mirror symmetry and loop operators
journal, November 2015
- Assel, Benjamin; Gomis, Jaume
- Journal of High Energy Physics, Vol. 2015, Issue 11
Remarks on A-branes, mirror symmetry, and the Fukaya category
journal, October 2003
- Kapustin, Anton; Orlov, Dmitri
- Journal of Geometry and Physics, Vol. 48, Issue 1
A link invariant from the symplectic geometry of nilpotent slices
journal, September 2006
- Seidel, Paul; Smith, Ivan
- Duke Mathematical Journal, Vol. 134, Issue 3
Knot homology via derived categories of coherent sheaves, I: The $\mathfrak{sl}(2)$ -case
journal, April 2008
- Cautis, Sabin; Kamnitzer, Joel
- Duke Mathematical Journal, Vol. 142, Issue 3
Knot homology via derived categories of coherent sheaves II, $\mathfrak{sl}_{m}$ case
journal, July 2008
- Cautis, Sabin; Kamnitzer, Joel
- Inventiones mathematicae, Vol. 174, Issue 1
Knot invariants from four-dimensional gauge theory
journal, January 2012
- Gaiotto, Davide; Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 16, Issue 3
Fukaya Categories and Picard–Lefschetz Theory
book, January 2008
- Seidel, Paul
- European Mathematical Society - EMS
AGT on the S-duality wall
journal, December 2010
- Hosomichi, Kazuo; Lee, Sungjay; Park, Jaemo
- Journal of High Energy Physics, Vol. 2010, Issue 12
Wave-equation scattering in even-dimensional spaces
journal, January 1976
- Adamyan, V. M.
- Functional Analysis and Its Applications, Vol. 10, Issue 1
𝒩 = 4 Superconformal Chern-Simons theories with hyper and twisted hyper multiplets
journal, July 2008
- Hosomichi, Kazuo; Lee, Ki-Myeong; Lee, Sangmin
- Journal of High Energy Physics, Vol. 2008, Issue 07
Phases of N = 2 theories in two dimensions
journal, August 1993
- Witten, Edward
- Nuclear Physics B, Vol. 403, Issue 1-2
Morse Theory and Tilting Sheaves
journal, January 2006
- Nadler, David
- Pure and Applied Mathematics Quarterly, Vol. 2, Issue 3
Quadratic duals, Koszul dual functors, and applications
journal, October 2008
- Mazorchuk, Volodymyr; Ovsienko, Serge; Stroppel, Catharina
- Transactions of the American Mathematical Society, Vol. 361, Issue 03
Gale duality and Koszul duality
journal, November 2010
- Braden, Tom; Licata, Anthony; Proudfoot, Nicholas
- Advances in Mathematics, Vol. 225, Issue 4
Hypertoric category <mml:math altimg="si1.gif" display="inline" 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">O</mml:mi></mml:math>
journal, October 2012
- Braden, Tom; Licata, Anthony; Proudfoot, Nicholas
- Advances in Mathematics, Vol. 231, Issue 3-4
Isomorphisms of quantizations via quantization of resolutions
journal, October 2012
- Losev, Ivan
- Advances in Mathematics, Vol. 231, Issue 3-4
Supersymmetric Vacua and Bethe Ansatz
journal, July 2009
- Nekrasov, Nikita A.; Shatashvili, Samson L.
- Nuclear Physics B - Proceedings Supplements, Vol. 192-193
On three dimensional quiver gauge theories and integrability
journal, May 2013
- Gaiotto, Davide; Koroteev, Peter
- Journal of High Energy Physics, Vol. 2013, Issue 5
Knot invariants and topological strings
journal, June 2000
- Ooguri, Hirosi; Vafa, Cumrun
- Nuclear Physics B, Vol. 577, Issue 3
Khovanov-Rozansky Homology and Topological Strings
journal, October 2005
- Gukov, Sergei; Schwarz, Albert; Vafa, Cumrun
- Letters in Mathematical Physics, Vol. 74, Issue 1
Sequencing BPS spectra
journal, March 2016
- Gukov, Sergei; Nawata, Satoshi; Saberi, Ingmar
- Journal of High Energy Physics, Vol. 2016, Issue 3
Matrix factorizations and link homology
journal, January 2008
- Khovanov, Mikhail; Rozansky, Lev
- Fundamenta Mathematicae, Vol. 199, Issue 1
Matrix factorizations and link homology II
journal, January 2008
- Khovanov, Mikhail; Rozansky, Lev
- Geometry & Topology, Vol. 12, Issue 3
An E 7 surprise
journal, October 2012
- Dimofte, Tudor; Gaiotto, Davide
- Journal of High Energy Physics, Vol. 2012, Issue 10
On mirror symmetry in three dimensional Abelian gauge theories
journal, April 1999
- Kapustin, Anton; Strassler, Matthew J.
- Journal of High Energy Physics, Vol. 1999, Issue 04
Derived equivalence for quantum symplectic resolutions
journal, October 2013
- McGerty, Kevin; Nevins, Thomas
- Selecta Mathematica, Vol. 20, Issue 2
Supersymmetry and Morse theory
journal, January 1982
- Witten, Edward
- Journal of Differential Geometry, Vol. 17, Issue 4
Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry
journal, August 2001
- Hori, Kentaro; Kapustin, Anton
- Journal of High Energy Physics, Vol. 2001, Issue 08
Monopole Operators and Mirror Symmetry in Three Dimensions
journal, December 2002
- Borokhov, Vadim; Kapustin, Anton; Wu, Xinkai
- Journal of High Energy Physics, Vol. 2002, Issue 12
Monopole operators and Hilbert series of Coulomb branches of 3d $ \mathcal{N} $ = 4 gauge theories
journal, January 2014
- Cremonesi, Stefano; Hanany, Amihay; Zaffaroni, Alberto
- Journal of High Energy Physics, Vol. 2014, Issue 1
Supersymmetric Yang-Mills theory and integrable systems
journal, February 1996
- Donagi, Ron; Witten, Edward
- Nuclear Physics B, Vol. 460, Issue 2
Quantal Phase Factors Accompanying Adiabatic Changes
journal, March 1984
- Berry, M. V.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 392, Issue 1802
A geometric Jacquet functor
journal, November 2004
- Emerton, M.; Nadler, D.; Vilonen, K.
- Duke Mathematical Journal, Vol. 125, Issue 2
Special Transverse Slices and Their Enveloping Algebras
journal, September 2002
- Premet, Alexander
- Advances in Mathematics, Vol. 170, Issue 1
A Remark on Rational Cherednik Algebras and Differential Operators on the Cyclic Quiver
journal, February 2006
- Gordon, Iain
- Glasgow Mathematical Journal, Vol. 48, Issue 01
Harish–Chandra homomorphisms and symplectic reflection algebras for wreath-products
journal, June 2007
- Etingof, Pavel; Gan, Wee Liang; Ginzburg, Victor
- Publications mathématiques de l'IHÉS, Vol. 105, Issue 1
On classification ofN=2 supersymmetric theories
journal, December 1993
- Cecotti, Sergio; Vafa, Cumrun
- Communications in Mathematical Physics, Vol. 158, Issue 3
Topological—anti-topological fusion
journal, December 1991
- Cecotti, Sergio; Vafa, Cumrun
- Nuclear Physics B, Vol. 367, Issue 2
A dilatonic deformation of AdS 5 and its field theory dual
journal, May 2003
- Bak, Dongsu; Gutperle, Michael; Hirano, Shinji
- Journal of High Energy Physics, Vol. 2003, Issue 05
Janus configurations, Chern-Simons couplings, and The θ-Angle in $ \mathcal{N} = 4 $ super Yang-Mills theory
journal, June 2010
- Gaiotto, Davide; Witten, Edward
- Journal of High Energy Physics, Vol. 2010, Issue 6
Quantum Cohomology of Flag Manifolds G/B and Quantum Toda Lattices
journal, January 1999
- Kim, Bumsig
- The Annals of Mathematics, Vol. 149, Issue 1
Quantum cohomology of partial flag manifolds $$F_{n_1 } \ldots _{n_k }$$
journal, June 1995
- Astashkevich, Alexander; Sadov, Vladimir
- Communications in Mathematical Physics, Vol. 170, Issue 3
Quantum cohomology of flag manifolds and Toda lattices
journal, April 1995
- Givental, Alexander; Kim, Bumsig
- Communications in Mathematical Physics, Vol. 168, Issue 3
Yangians and quantizations of slices in the affine Grassmannian
journal, January 2014
- Kamnitzer, Joel; Webster, Ben; Weekes, Alex
- Algebra & Number Theory, Vol. 8, Issue 4
Constructible sheaves and the Fukaya category
journal, September 2008
- Nadler, David; Zaslow, Eric
- Journal of the American Mathematical Society, Vol. 22, Issue 1
Categorifications and cyclotomic rational double affine Hecke algebras
journal, September 2015
- Rouquier, Raphaël; Shan, Peng; Varagnolo, Michela
- Inventiones mathematicae, Vol. 204, Issue 3
Koszul duality of affine Kac–Moody algebras and cyclotomic rational double affine Hecke algebras
journal, September 2014
- Shan, P.; Varagnolo, M.; Vasserot, E.
- Advances in Mathematics, Vol. 262
Gauge theory and knot homologies
journal, May 2007
- Gukov, S.
- Fortschritte der Physik, Vol. 55, Issue 5-7
Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics
journal, May 1997
- Hanany, Amihay; Witten, Edward
- Nuclear Physics B, Vol. 492, Issue 1-2
Topological quantum field theory
journal, September 1988
- Witten, Edward
- Communications in Mathematical Physics, Vol. 117, Issue 3
Topological sigma models
journal, September 1988
- Witten, Edward
- Communications in Mathematical Physics, Vol. 118, Issue 3
Matrix factorizations and link homology II
text, January 2008
- Mikhail, Khovanov,; Lev, Rozansky,
- The University of North Carolina at Chapel Hill University Libraries
Homological algebra of knots and BPS states
conference, May 2013
- Gukov, Sergei; Stošić, Marko
- Low-dimensional manifolds and high-dimensional categories -- A conference in honor of Michael Hartley Freedman, Geometry & Topology Monographs
Supersymmetric vacua and Bethe ansatz
text, January 2009
- Nekrasov, Nikita A.; Shatashvili, Samson L.
- arXiv
Quantization of Integrable Systems and Four Dimensional Gauge Theories
text, January 2009
- Nekrasov, Nikita A.; Shatashvili, Samson L.
- arXiv
The Omega Deformation, Branes, Integrability, and Liouville Theory
text, January 2010
- Nekrasov, Nikita; Witten, Edward
- arXiv
Isomorphisms of quantizations via quantization of resolutions
preprint, January 2010
- Losev, Ivan
- arXiv
Derived equivalence for quantum symplectic resolutions
preprint, January 2011
- McGerty, Kevin; Nevins, Thomas
- arXiv
3-Manifolds and 3d Indices
preprint, January 2011
- Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei
- arXiv
Holomorphic Blocks in Three Dimensions
text, January 2012
- Beem, Christopher; Dimofte, Tudor; Pasquetti, Sara
- arXiv
On Three Dimensional Quiver Gauge Theories and Integrability
text, January 2013
- Gaiotto, Davide; Koroteev, Peter
- arXiv
RG Domain Walls and Hybrid Triangulations
preprint, January 2013
- Dimofte, Tudor; Gaiotto, Davide; van der Veen, Roland
- arXiv
Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries
text, January 2013
- Sugishita, Sotaro; Terashima, Seiji
- arXiv
Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
text, January 2013
- Cremonesi, Stefano; Hanany, Amihay; Zaffaroni, Alberto
- arXiv
A Dilatonic Deformation of AdS_5 and its Field Theory Dual
text, January 2003
- Bak, Dongsu; Gutperle, Michael; Hirano, Shinji
- arXiv
Khovanov-Rozansky Homology and Topological Strings
text, January 2004
- Gukov, Sergei; Schwarz, Albert; Vafa, Cumrun
- arXiv
Electric-Magnetic Duality And The Geometric Langlands Program
preprint, January 2006
- Kapustin, Anton; Witten, Edward
- arXiv
Mirror Symmetry in Three Dimensional Gauge Theories
text, January 1996
- Intriligator, K.; Seiberg, N.
- arXiv
Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics
text, January 1996
- Seiberg, Nathan
- arXiv
Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
text, January 1996
- Morrison, David R.; Seiberg, Nathan
- arXiv
Small Instantons, del Pezzo Surfaces and Type I' theory
text, January 1996
- Douglas, M. R.; Katz, S.; Vafa, C.
- arXiv
Hyper-Kahler Geometry and Invariants of Three-Manifolds
text, January 1996
- Rozansky, L.; Witten, E.
- arXiv
Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces
text, January 1997
- Intriligator, K.; Morrison, D. R.; Seiberg, N.
- arXiv
D-particle bound states and generalized instantons
text, January 1998
- Moore, G.; Nekrasov, N.; Shatashvili, S.
- arXiv
Matrix factorizations and link homology II
text, January 2005
- Khovanov, Mikhail; Rozansky, Lev
- arXiv
Quadratic duals, Koszul dual functors, and applications
text, January 2006
- Mazorchuk, Volodymyr; Ovsienko, Serge; Stroppel, Catharina
- arXiv
Works referencing / citing this record:
Vertex Operator Algebras and 3d N $$ \mathcal{N} $$ = 4 gauge theories
journal, May 2019
- Costello, Kevin; Gaiotto, Davide
- Journal of High Energy Physics, Vol. 2019, Issue 5
Twisted indices of 3d N $$ \mathcal{N} $$ = 4 gauge theories and enumerative geometry of quasi-maps
journal, July 2019
- Bullimore, Mathew; Ferrari, Andrea; Kim, Heeyeon
- Journal of High Energy Physics, Vol. 2019, Issue 7
Deformation Quantization and Superconformal Symmetry in Three Dimensions
journal, February 2017
- Beem, Christopher; Peelaers, Wolfger; Rastelli, Leonardo
- Communications in Mathematical Physics, Vol. 354, Issue 1
The Coulomb Branch of 3d $${\mathcal{N}= 4}$$ N = 4 Theories
journal, June 2017
- Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide
- Communications in Mathematical Physics, Vol. 354, Issue 2
Boundaries and supercurrent multiplets in 3D Landau-Ginzburg models
journal, June 2019
- Brunner, Ilka; Schulz, Jonathan; Tabler, Alexander
- Journal of High Energy Physics, Vol. 2019, Issue 6
Twisted Hilbert spaces of 3d supersymmetric gauge theories
journal, August 2018
- Bullimore, Mathew; Ferrari, Andrea
- Journal of High Energy Physics, Vol. 2018, Issue 8
Deformation quantization and superconformal symmetry in three dimensions
text, January 2016
- Beem, Christopher; Peelaers, Wolfger; Rastelli, Leonardo
- arXiv