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Non-perturbative approaches to the quantum Seiberg-Witten curve

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arxiv 1908.07065 v3 pith:QJU7W2V2 submitted 2019-08-19 hep-th math-phmath.MP

Alba Grassi , Jie Gu , Marcos Marino This is my paper
classification hep-thmath-phmath.MP
keywords operatorquantumapproachescurveequationsmathieumodifiednon-perturbative
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We study various non-perturbative approaches to the quantization of the Seiberg-Witten curve of ${\cal N}=2$, $SU(2)$ super Yang-Mills theory, which is closely related to the modified Mathieu operator. The first approach is based on the quantum WKB periods and their resurgent properties. We show that these properties are encoded in the TBA equations of Gaiotto-Moore-Neitzke determined by the BPS spectrum of the theory, and we relate the Borel-resummed quantum periods to instanton calculus. In addition, we use the TS/ST correspondence to obtain a closed formula for the Fredholm determinant of the modified Mathieu operator. Finally, by using blowup equations, we explain the connection between this operator and the $\tau$ function of Painleve $\rm III$.

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Cited by 12 Pith papers

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