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Exact WKB analysis and TBA equations for the Mathieu equation

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arxiv 2002.06829 v2 pith:ZMXNZIRN submitted 2020-02-17 hep-th math-phmath.MPquant-ph

Keita Imaizumi This is my paper
classification hep-thmath-phmath.MPquant-ph
keywords equationsequationmathieuperiodscalculatecouplingexactquantum
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We derive the Thermodynamic Bethe Ansatz (TBA) equations for the exact WKB periods of the Mathieu equation in the weak coupling region. We will use the TBA equations to calculate the quantum corrections to the WKB periods, which are regarded the quantum periods of $\mathcal{N} = 2$ $SU(2)$ super Yang-Mills theory at strong coupling. We calculate the effective central charge of the TBA equations, which is found to be proportional to the coefficient of the one-loop beta function of the 4d theory. We also study the spectral problem for the Mathieu equation based on the TBA equations numerically.

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Cited by 2 Pith papers

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