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- W4385220986 abstract "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 ) $${mathcal N}=2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> 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 conformal , then the series has at least a finite radius of convergence, while if it is asymptotically free it has infinite radius of convergence. Via AGT correspondence, this implies that the related irregular conformal blocks of $$W_N$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> 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 analyze the convergence properties of the corresponding Painlevé $$tau $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>τ</mml:mi> </mml:math> -functions." @default.
- W4385220986 created "2023-07-25" @default.
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- W4385220986 date "2023-07-24" @default.
- W4385220986 modified "2023-10-18" @default.
- W4385220986 title "On the Convergence of Nekrasov Functions" @default.
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- W4385220986 doi "https://doi.org/10.1007/s00023-023-01349-3" @default.
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