Boundaries, mirror symmetry, and symplectic duality in 3d N=4 gauge theory

A bstract We introduce several families of N = 2 , 2 UV boundary conditions in 3d N = 4 gaugetheoriesandstudytheirIRimagesinsigma-modelstotheHiggsandCoulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and...

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Vydané v:The journal of high energy physics Ročník 2016; číslo 10
Hlavní autori: Bullimore, Mathew, Dimofte, Tudor, Gaiotto, Davide, Hilburn, Justin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 20.10.2016
Springer Berlin
Predmet:
Classical and Quantum Gravitation
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Elementary Particles
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Solitons Monopoles and Instantons
String Theory
Supersymmetric Gauge Theory
Supersymmetry and Duality
Topological Field Theories
Topological Field Theories
Supersymmetry and Duality
Supersymmetric gauge theory
Solitons Monopoles and Instantons
ISSN:1029-8479, 1029-8479
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Popis
Shrnutí:A bstract We introduce several families of N = 2 , 2 UV boundary conditions in 3d N = 4 gaugetheoriesandstudytheirIRimagesinsigma-modelstotheHiggsandCoulomb 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, respec-tively, 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.
Bibliografia:SC0009988; 335739; 306260
USDOE Office of Science (SC), High Energy Physics (HEP)
European Research Council (ERC)
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP10(2016)108