论文标题
四点球形结构块的模块化线性微分方程
Modular linear differential equations for four-point sphere conformal blocks
论文作者
论文摘要
我们构建模块化线性微分方程（MLDES）W.R.T。模块基团的亚组，其溶液是Virasoro共形块，出现在球体上的交叉对称4点相关器的扩展中。这使用交叉转换和模块化转换之间的连接。我们专门关注二阶MLDE，其中包括相关器中所有相同和成对相同的操作员的情况。中央电荷，上述运算符的尺寸和中间的尺寸是根据在此类MLDE中发生的参数表示的。在这样做的过程中，将$ q $ $ Q $ - 对MLDES的解决方案的扩展与Virasoro块的解决方案进行了比较；因此，Zamolodchikov的椭圆递归公式提供了重要的输入。使用各个亚组的动作，已经在MLDE参数方面建立了涉及相关三点系数的引导程序方程。我们介绍了与BPZ和新型非BPZ方程以及单一和非单身CFT相对应的MLDE的明确例子。
We construct modular linear differential equations (MLDEs) w.r.t. subgroups of the modular group whose solutions are Virasoro conformal blocks appearing in the expansion of a crossing symmetric 4-point correlator on the sphere. This uses a connection between crossing transformations and modular transformations. We focus specifically on second order MLDEs with the cases of all identical and pairwise identical operators in the correlator. The central charge, the dimensions of the above operators and those of the intermediate ones are expressed in terms of parameters that occur in such MLDEs. In doing so, the $q$-expansions of the solutions to the MLDEs are compared with those of Virasoro blocks; hence, Zamolodchikov's elliptic recursion formula provides an important input. Using the actions of respective subgroups, bootstrap equations involving the associated 3-point coefficients have been set up and solved as well in terms of the MLDE parameters. We present explicit examples of MLDEs corresponding to BPZ and novel non-BPZ equations, as well as unitary and non-unitary CFTs.
