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Analyticity of Nekrasov Partition Functions

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arxiv 1709.05232 v3 pith:LWPAWHQN submitted 2017-09-15 math-ph math.MP

Giovanni Felder , Martin Müller-Lennert This is my paper · ORCID
classification math-phmath.MP
keywords functionsnekrasovpartitionanalyticityinstantonprovealgebraconvergence
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We prove that the K-theoretic Nekrasov instanton partition functions have a positive radius of convergence in the instanton counting parameter and are holomorphic functions of the Coulomb parameters in a suitable domain. We discuss the implications for the AGT correspondence and the analyticity of the norm of Gaiotto states for the deformed Virasoro algebra. The proof is based on random matrix techniques and relies on an integral representation of the partition function, due to Nekrasov, which we also prove.

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Cited by 2 Pith papers

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  1. Probing Non-Graviton Spectra in $\mathcal{N}=4$ SYM via BMN truncation and S-Duality

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    The BMN index of N=4 SYM contains universal non-graviton bosonic towers, and the S-duality mismatch between SO(7) and Sp(3) pinpoints a non-graviton cohomology.

  2. Exponentiation of higher-point and higher-genus Virasoro conformal blocks in the semiclassical limit

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Extends the exponentiation of Virasoro conformal blocks in the semiclassical limit to higher-point and higher-genus cases at the level of formal power series using an extended oscillator method.

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