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Q-operators for the Ruijsenaars model

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arxiv 2503.18057 v1 pith:4PKXOPDC submitted 2025-03-23 math-ph math.CAmath.MPnlin.SI

Eric Rains , Hjalmar Rosengren This is my paper
classification math-phmath.CAmath.MPnlin.SI
keywords ellipticq-operatorshypergeometricmodelruijsenaarsadmitsalternativeappear
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We prove that the Ruijsenaars model admits a one-parameter commuting family of Q-operators. The commutativity is equivalent to an elliptic hypergeometric integral transformation that was conjectured by Gadde et al., and has an alternative interpretation in terms of S-duality for quiver gauge theories. We present two proofs of this conjecture, one using the elliptic Macdonald polynomials of Langmann et al., and one using known results on elliptic hypergeometric integrals. We also explain how the Noumi-Sano operators appear as degenerations of Q-operators.

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  1. Generalized Schur partition functions and RG flows

    hep-th 2025-06 conditional novelty 6.0 of 10

    The generalized Schur partition function of SU(2) N_f=4 SQCD, evaluated at alpha = h^vee_g / 6, reproduces the Schur indices of every SCFT in the Deligne-Cvitanovic rank-one series.

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