Modular properties of algebraic structures arising from conformal field theory

目前，我正在寻找是否有可能找到一个模块化的转换公式，在不同的二维CFTs保守的费用。我从自由费米子理论开始，在费米子模式下，KdV电荷简化为双线性。这使我能够计算KdV电荷的任何幂的期望值，然后找到这些期望值的模变换。现在我将开始研究其他理论，从一些最小模型开始，看看KdV电荷的模变换是否可以在这些理论中确定。首先，我将看看我是否可以计算KdV电荷的期望值，如果这是可能的，那么我将尝试找到这些期望值的模变换。最终的目标是找到这些期望值的一般转换公式，看看是否有任何跨不同理论的一般特征。

Currently I am looking at whether it is possible to find a modular transformation formula for conserved charges in different 2d CFTs. I started with the free fermion theory where the the KdV charges simplify to be bilinear in the fermion modes. This allowed me to calculate the expectation values for any power of the KdV charges and then find the modular transform of these expectation values. I will now start to look at other theories, starting with some of the minimal models to see if the modular transform of the KdV charges can be determined in these theories. Initially I will see if I can compute the expectation value of the KdV charges and if this is possible then I will try to find the modular transform of these expectation values. The final aim is to find a general transformation formula for these expectation values and see if there are any general features that hold across different theories.