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

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:
 [1] ;  [2] ;  [3] ;  [4]
  1. Univ. of Oxford (United Kingdom). Mathematical Inst.; Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
  2. 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
  3. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  4. Univ. of Oregon, Eugene, OR (United States). Dept. of Mathematics
Publication Date:
Grant/Contract Number:
SC0009988; 335739; 306260
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
Research Org:
Univ. of Oxford (United Kingdom)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); European Research Council (ERC)
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
OSTI Identifier:
1358546