Quarter-indices for basic ortho-symplectic corners

TL;DR

This paper computes exact quarter-indices for orthogonal and symplectic gauge theory corners, demonstrating S-duality and linking indices to W-algebras and Lie superalgebras.

Contribution

It provides closed-form expressions for quarter-indices of Y-junctions in 4d super Yang-Mills with orthogonal and symplectic groups, and explores their algebraic interpretations.

Findings

Exact closed-form quarter-indices for Y-junctions obtained.

Indices match between dual configurations, supporting S-duality.

In special limits, indices relate to W-algebras and superalgebras.

Abstract

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