Mirror symmetry of 3d $\mathcal{N}=4$ gauge theories and supersymmetric indices

Abstract

We compute supersymmetric indices to test mirror symmetry of three-dimensional $\mathcal{N}=4$ gauge theories and dualities of half-BPS enriched boundary conditions and interfaces in four-dimensional $\mathcal{N}=4$ Super Yang-Mills theory. We find the matching of indices as strong evidences for various dualities of the 3d interfaces conjectured by Gaiotto and Witten under the action of S-duality in Type IIB string theory.

arXiv comment57 pages, 16 figures, v3: published version in Physical Review D

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• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• Dualities of Corner Configurations and Supersymmetric Indices
• Topological Correlators and Surface Defects from Equivariant Cohomology
• Dualities and flavored indices of M2-brane SCFTs
• Giant graviton expansions and ETW brane
• Orbifold ETW brane and half-indices
• M2-M5 giant graviton expansions
• ADHM Wilson line defect indices
• The Giant Graviton Expansion
• S-duality of boundary lines in $\mathcal{N}=4$ SYM theories and supersymmetric indices
• Abelian dualities and line defect indices for 3d gauge theories
• Mixed moduli in 3d N=4 higher-genus quivers
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs
• Interface line operators in $\mathcal{N}=4$ SYM theories and supersymmetric indices