Deformed Schur Indices of BCD-type for N=4 Super Yang-Mills and Symmetric Functions

TL;DR

This paper studies the deformed Schur index in N=4 super Yang-Mills theories with SO and Sp gauge groups, expressing it through advanced symmetric functions, and tests duality properties.

Contribution

It introduces a new formulation of the deformed Schur index using Koornwinder and Macdonald polynomials for BCD-type gauge groups, extending previous calculations.

Findings

Explicit formulas for low rank gauge groups

Results in special limits of the index

Verification of S-duality tests

Abstract

We investigate the deformed Schur index in four dimensional N=4 super Yang-Mills theories with $SO$ and $Sp$ gauge groups, generalizing Hatsuda's recent calculations. We express the deformed Schur index as integrals of Koornwinder polynomials and Macdonald polynomials, then perform the integrals in terms of the normalization constants of Macdonald polynomials. We provide explicit results for some low rank gauge groups and for expansion in a $u$ parameter. We discuss various special limits and the tests of S-duality.