Quarter-indices for basic ortho-symplectic corners

A bstract We study supersymmetric quarter-indices for corner configurations in 4d $$ \mathcal{N} $$ 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 $$ \mathfrak{osp}\left(1|2N\right) $$ osp 1 2 N as the corner vertex operator algebras.