WKB periods for higher order ODE and TBA equations
WKB periods for higher order ODE and TBA equations
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DOI：
10.1007/jhep10(2021)167
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发表时间：
2021-04
影响因子：
5.4
通讯作者：
K. Ito;Takayasu Kondo;Kohei Kuroda;Hongfei Shu
中科院分区：
文献类型：
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作者：
K. Ito;Takayasu Kondo;Kohei Kuroda;Hongfei Shu
研究由仿射Toda场方程线性问题的共形极限得到的(r+1)阶常微分方程解的WKB周期。我们利用Picard-Fuchs算符计算了量子修正。ODE/IM对应给出了满足与Lie代数Ar有关的热力学Bethe ansatz(TBA)方程的解的Wronskian与Y-函数之间的关系.对于二次势，我们提出了一个证明Y-函数的对数与WKB周期之间的等价性的公式，并通过数值求解TBA方程得到了证实.
We study the WKB periods for the (r+ 1)-th order ordinary differential equation (ODE) which is obtained by the conformal limit of the linear problem associated with theaffine Toda field equation. We compute the quantum corrections by using the Picard-Fuchs operators. The ODE/IM correspondence provides a relation between the Wronskians of the solutions and the Y-functions which satisfy the thermodynamic Bethe ansatz (TBA) equation related to the Lie algebra A r. For the quadratic potential, we propose a formula to show the equivalence between the logarithm of the Y-function and the WKB period, which is confirmed by solving the TBA equation numerically.