Intersecting Defects and Supergroup Gauge Theory

Abstract

We consider 5d supersymmetric gauge theories with unitary groups in the $\Omega$-background and study codim-2/4 BPS defects supported on orthogonal planes intersecting at the origin along a circle. The intersecting defects arise upon implementing the most generic Higgsing (geometric transition) to the parent higher dimensional theory, and they are described by pairs of 3d supersymmetric gauge theories with unitary groups interacting through 1d matter at the intersection. We explore the relations between instanton and generalized vortex calculus, pointing out a duality between intersecting defects subject to the $\Omega$-background and a deformation of supergroup gauge theories, the exact supergroup point being achieved in the self-dual or unrefined limit. Embedding our setup into refined topological strings and in the simplest case when the parent 5d theory is Abelian, we are able to identify the supergroup theory dual to the intersecting defects as the supergroup version of refined Chern-Simons theory via open/closed duality. We also discuss the BPS/CFT side of the correspondence, finding an interesting large rank duality with super-instanton counting.

v1: 50 pages; v2: 51 pages, added more references, minor comments and report n; v3: published version

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Cited by in corpus (9)

• Quantum toroidal algebras and solvable structures in gauge/string theory
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Gauge origami and quiver W-algebras
• $t{t}^{\ast }$ Toda equations for surface defects in $\mathcal{N}=2$ SYM and instanton counting for classical Lie groups
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Virasoro Constraint for Uglov Matrix Model
• 3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices
• Generalized Calogero-Moser system and supergroup gauge origami
• On refined Chern-Simons and refined ABJ matrix models