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Deformed Schur indices and Macdonald polynomials

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arxiv 2503.03952 v1 pith:FSSF6LDQ submitted 2025-03-05 hep-th math-phmath.MP

Yasuyuki Hatsuda This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords indexschurdeformedindiceslinemacdonaldoperatorpolynomials
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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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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM

    hep-th 2026-08 conditional novelty 7.0 of 10

    Exact finite-N superconformal indices with antisymmetric surface-defect insertions are obtained as bilateral free-fermion determinants on the t=q, p=uv locus, including complete one-charge correction towers.

  2. S-duality of boundary lines in $\mathcal{N}=4$ SYM theories and supersymmetric indices

    hep-th 2025-05 conditional novelty 7.0 of 10

    Boundary Wilson and 't Hooft line two-point functions in N=4 SYM match exactly under S-duality, with closed forms from Macdonald polynomials.

  3. Unitary matrix models, quantized symmetric functions and spin chain

    hep-th 2026-07 conditional novelty 6.0 of 10

    Unitary matrix models are mapped to vacuum correlators of quantized symmetric functions in the N-magnon sector of a spin chain via Schur orthogonality.

  4. Quiver superconformal index and giant gravitons: asymptotics and expansions

    hep-th 2025-09 conditional novelty 6.0 of 10

    For toric quiver theories, coefficients of the large-N superconformal index grow like exp(constant*sqrt(n)) times n^((m-5)/4) for the A-hat_m family, with polynomial growth for dP3 and Y^{p,0}.

  5. Modularity, 4d mirror symmetry, and VOA modules of 4d $\mathcal{N} = 2$ SCFTs with $a = c$

    hep-th 2025-05 conditional novelty 6.0 of 10

    The vacuum Schur-index modular orbit is proposed as the full VOA module-character space for several a=c theories, with a conjectured dimension formula 1+3ℓ(2+ℓ) for the T_{2,2ℓ+1} series.

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