论文标题
半经典保形块的扩展
Expansions for semiclassical conformal blocks
论文作者
论文摘要
我们提出了一个关系，即在不同的分支点处的常规和不规则半经典的共形块的扩展利用了BPZ解耦方程与异构粒子tau函数的对数衍生物的辅助参数之间的连接。我们通过考虑从黑洞线性化的扰动理论获得的汇合HEUN方程的两个特征值问题来支持这些关系。我们首先得出球体方程的较大频率膨胀，然后在数值上比较了从大频率扩展获得的Schwarzschild案例的激发准正常模式谱，并与从低频膨胀和文献中获得的schwarzschild案例进行比较，表明该关系在复杂的模量平面中呈一体依赖。
We propose a relation the expansions of regular and irregular semiclassical conformal blocks at different branch points making use of the connection between the accessory parameters of the BPZ decoupling equations to the logarithm derivative of isomonodromic tau functions. We give support for these relations by considering two eigenvalue problems for the confluent Heun equations obtained from the linearized perturbation theory of black holes. We first derive the large frequency expansion of the spheroidal equations, and then compare numerically the excited quasi-normal mode spectrum for the Schwarzschild case obtained from the large frequency expansion to the one obtained from the low frequency expansion and with the literature, indicating that the relations hold generically in the complex modulus plane.
