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

Bullimore, Mathew and Dimofte, Tudor and Gaiotto, Davide and Hilburn, Justin and Kim, Hee-Cheol (2016) 'Boundaries, mirror symmetry, and symplectic duality in 3d N=4 gauge theory.', Journal of high energy physics., 2016 (10). p. 108.


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.

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Publisher statement:© The Author(s) 2016 Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:30 September 2016
Date deposited:08 June 2018
Date of first online publication:20 October 2016
Date first made open access:08 June 2018

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