Deformed Schur indices and Macdonald polynomials

Yasuyuki Hatsuda

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arXiv · 2503.03952

Deformed Schur indices and Macdonald polynomials

Yasuyuki Hatsuda

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Abstract

The Schur index in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory with $U(N)$ gauge group has a natural two-parameter deformation. We find that a matrix integral in such a deformed Schur index can be exactly evaluated by using Macdonald polynomials. The resulting expression is a simple combinatorial summation over partitions. An extension to line operator indices is straightforward. In particular, for an anti-symmetric representation, the line operator index has a relatively simple form. We further discuss infinite $N$ analysis and finite $N$ giant graviton expansions.

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Yasuyuki Hatsuda. 2025-03-05. Deformed Schur indices and Macdonald polynomials. https://arxiv.org/abs/2503.03952

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