S-duality of boundary lines in $\mathcal{N}=4$ SYM theories and supersymmetric indices

Abstract

We analyze the supersymmetric defect indices of $\mathcal{N}=4$ super Yang Mills theories which are simultaneously decorated by the BPS line operators and the boundary conditions. We demonstrate that the two-point functions of the boundary 't Hooft lines of magnetic charges associated with the minuscule representations in the presence of the regular Nahm pole boundary conditions can be obtained by applying the Higgsing prescription to the half-indices of the Dirichlet boundary conditions. Accordingly, we find precise matching of the indices for pairs of the S-dual configurations with the Wilson lines and Neumann boundary conditions and those with the 't Hooft lines and the regular Nahm pole boundary conditions. Alternatively, we analytically compute the indices by means of the inner product of the Macdonald polynomials to find the exact closed-form expressions.

arXiv comment77 pages, v2: published version in JHEP

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Cited by in corpus (4)

• Abelian dualities and line defect indices for 3d gauge theories
• Boundary lines and Askey-Wilson type moments
• Interface line operators in $\mathcal{N}=4$ SYM theories and supersymmetric indices
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs