论文标题
MATHIEU方程的确切WKB分析和TBA方程
Exact WKB analysis and TBA equations for the Mathieu equation
论文作者
论文摘要
我们在弱耦合区域的MATHIEU方程的确切WKB时期中得出了热力学Bethe Ansatz（TBA）方程。我们将使用TBA方程来计算WKB期间的量子校正，这些量子被认为是$ \ Mathcal {n} = 2 $ $ su（2）$ super yang-mills理论在强耦合处。我们计算了TBA方程的有效中心电荷，该方程与4D理论的单环β函数系数成正比。我们还基于数值基于TBA方程的MATHIEU方程的光谱问题。
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.
