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.

arXiv comment51 pages, v3: published version in JHEP

References in corpus (27)

• An Index for 4 dimensional Super Conformal Theories
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Mirror Symmetry in Three Dimensional Gauge Theories
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Elliptic genera of 2d N=2 gauge theories
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Holomorphic Blocks in Three Dimensions
• On the Landau-Ginzburg Description of $N=2$ Minimal Models
• 2d Index and Surface operators
• Factorisation of N = 2 theories on the squashed 3-sphere
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• Aspects of N_{T}\geq 2 Topological Gauge Theories and D-Branes
• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• Elliptic Genera and N=2 Superconformal Field Theory
• Dual Boundary Conditions in 3d SCFT's
• Vertex Operator Algebras and 3d N=4 gauge theories
• An E7 Surprise
• Hypertoric category O
• Mirror symmetry and line operators
• Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras
• Surface Defect Indices and 2d-4d BPS States
• (0,4) brane box models
• Sphere correlation functions and Verma modules
• Abelian dualities of $\mathcal{N}=(0,4)$ boundary conditions
• Dualities of Corner Configurations and Supersymmetric Indices
• 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
• Dualities and flavored indices of M2-brane SCFTs
• 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