Theoretical analysis reveals exact closed-form quarter-indices for orthosymplectic corner configurations, supporting S-duality and connections to vertex operator algebras.
A bstract We study supersymmetric quarter-indices for corner configurations in 4d N N = 4 super Yang-Mills theory with orthogonal and symplectic gauge groups. For the basic Y-junctions, we obtain exact closed-form expressions for the indices by making use of the Gustafson type integral formula and the Higgsing method. We demonstrate the equality of the quarter-indices between dual configurations, providing evidence for S-duality of the corner configurations. In the special fugacity limit, the indices admit an interpretation in terms of the vacuum characters of the W-algebras of type BCD, and the Lie superalgebra osp(1|2N) osp 1 2 N as the corner vertex operator algebras.
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Hatsuda et al. (2026) studied this question.
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