Abelian mirror symmetry of \(\mathcal{N} = (2, 2)\) boundary conditions. (English) Zbl 1461.81131
Summary: 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.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
Keywords:
differential and algebraic geometry; duality in gauge field theories; supersymmetric gauge theory; supersymmetry and dualityReferences:
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