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- W4311558021 abstract "In this note we present some results on the convergence of Nekrasov partition functions as power series in the instanton counting parameter. We focus on $U(N)$ ${mathcal N}=2$ gauge theories in four dimensions with matter in the adjoint and in the fundamental representations of the gauge group respectively and find rigorous lower bounds for the convergence radius in the two cases: if the theory is {it conformal}, then the series has at least a {it finite} radius of convergence, while if it is {it asymptotically free} it has {it infinite} radius of convergence. Via AGT correspondence, this implies that the related irregular conformal blocks of $W_N$ algebrae admit a power expansion in the modulus converging in the whole plane. By specifying to the $SU(2)$ case, we apply our results to analyse the convergence properties of the corresponding Painlev'e $tau$-functions." @default.
- W4311558021 created "2022-12-27" @default.
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- W4311558021 date "2022-12-13" @default.
- W4311558021 modified "2023-10-14" @default.
- W4311558021 title "On the convergence of Nekrasov functions" @default.
- W4311558021 doi "https://doi.org/10.48550/arxiv.2212.06741" @default.
- W4311558021 hasPublicationYear "2022" @default.
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