March 3, 2026Open Access

Deformed Schur indices of BCD-type for N=4 super Yang-Mills and symmetric functions

Key Points

The deformed schur index is formulated through integrals of koornwinder and macdonald polynomials, leading to multiple insights.
Explicit results derived for low rank gauge groups indicate patterns in s-duality, with implications for theoretical physics.
Investigations express the deformed Schur index in terms of normalization constants, enhancing understanding of gauge theories.
The analysis discusses special limits that may further clarify the relationships between different gauge groups.

Abstract

A bstract 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.

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