Abelian mirror symmetry of $\mathcal{N}=(2,2)$ boundary conditions

Abstract

We evaluate half-indices of $\mathcal{N}=(2,2)$ half-BPS boundary conditions in 3d $\mathcal{N}=4$ supersymmetric Abelian gauge theories. We confirm that the Neumann boundary condition is dual to the generic Dirichlet boundary condition for its mirror theory as the half-indices perfectly match with each other. We find that a naive mirror symmetry between the exceptional Dirichlet boundary conditions defining the Verma modules of the quantum Coulomb and Higgs branch algebras does not always hold. The triangular matrix obtained from the elliptic stable envelope describes the precise mirror transformation of a collection of half-indices for the exceptional Dirichlet boundary conditions.

51 pages, v3: published version in JHEP

References in corpus (3)

• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Sphere correlation functions and Verma modules
• Singular BPS boundary conditions in $\mathcal{N}=(2,2)$ supersymmetric gauge theories

Cited by in corpus (7)

• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
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• Seiberg-like dualities for orthogonal and symplectic 3d $\mathcal{N}=2$ gauge theories with boundaries
• 3d exceptional gauge theories and boundary confinement
• Abelian dualities and line defect indices for 3d gauge theories
• Line defect half-indices of $SU(N)$ Chern-Simons theories
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs