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

Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; Hilburn, Justin

doi:10.1007/JHEP10(2016)108

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

Journal Article · Thu Oct 20 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP10(2016)108· OSTI ID:1358546

Bullimore, Mathew ^[1]; Dimofte, Tudor ^[2]; Gaiotto, Davide ^[3]; Hilburn, Justin ^[4]

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

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.

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Research Organization:: Univ. of Oxford (United Kingdom)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); European Research Council (ERC)

Grant/Contract Number:: SC0009988; 335739; 306260

OSTI ID:: 1358546

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 10; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 62 works

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Deformation Quantization and Superconformal Symmetry in Three Dimensions Beem, Christopher; Peelaers, Wolfger; Rastelli, Leonardo Communications in Mathematical Physics, Vol. 354, Issue 1 https://doi.org/10.1007/s00220-017-2845-6	journal	February 2017
The Coulomb Branch of 3d $${\mathcal{N}= 4}$$ N = 4 Theories Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide Communications in Mathematical Physics, Vol. 354, Issue 2 https://doi.org/10.1007/s00220-017-2903-0	journal	June 2017
Boundaries and supercurrent multiplets in 3D Landau-Ginzburg models Brunner, Ilka; Schulz, Jonathan; Tabler, Alexander Journal of High Energy Physics, Vol. 2019, Issue 6 https://doi.org/10.1007/jhep06(2019)046	journal	June 2019
Twisted Hilbert spaces of 3d supersymmetric gauge theories Bullimore, Mathew; Ferrari, Andrea Journal of High Energy Physics, Vol. 2018, Issue 8 https://doi.org/10.1007/jhep08(2018)018	journal	August 2018
Deformation quantization and superconformal symmetry in three dimensions Beem, Christopher; Peelaers, Wolfger; Rastelli, Leonardo arXiv https://doi.org/10.48550/arxiv.1601.05378	text	January 2016

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

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