Dual boundary conditions reduce Omega-deformed 3d N = 4 localization to integrals over Hecke modification spaces, recovering the BFN Coulomb branch algebra, boundary modules, and cylindrical KLRW algebras.
Geometric Langlands And The Equations Of Nahm And Bogomolny
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abstract
Geometric Langlands duality relates a representation of a simple Lie group $G^\vee$ to the cohomology of a certain moduli space associated with the dual group $G$. In this correspondence, a principal $SL_2$ subgroup of $G^\vee$ makes an unexpected appearance. Why this happens can be explained using gauge theory, as we will see in this article, with the help of the equations of Nahm and Bogomolny. (Based on a lecture at Geometry and Physics: Atiyah 80, Edinburgh, April 2009.)
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Coulomb Branches in 3d $\mathcal{N} = 4$ Revisited
Dual boundary conditions reduce Omega-deformed 3d N = 4 localization to integrals over Hecke modification spaces, recovering the BFN Coulomb branch algebra, boundary modules, and cylindrical KLRW algebras.