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Boundaries, Mirror Symmetry, and Symplectic Duality in 3d N=4 Gauge Theory

Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; Hilburn, Justin; Kim, Hee-Cheol

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Tudor Dimofte

Davide Gaiotto

Justin Hilburn

Hee-Cheol Kim


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.


Bullimore, M., Dimofte, T., Gaiotto, D., Hilburn, J., & Kim, H. (2016). Boundaries, Mirror Symmetry, and Symplectic Duality in 3d N=4 Gauge Theory. Journal of High Energy Physics, 2016(10), Article 108.

Journal Article Type Article
Acceptance Date Sep 30, 2016
Online Publication Date Oct 20, 2016
Publication Date Oct 20, 2016
Deposit Date Jun 7, 2018
Publicly Available Date Jun 8, 2018
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2016
Issue 10
Article Number 108


Published Journal Article (4.9 Mb)

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Copyright 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.

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