Modular properties of algebraic structures arising from conformal field theory

目前，我正在研究是否有可能在不同的二维cft中找到守恒电荷的模变换公式。我从自由费米子理论开始在费米子模式中，KdV电荷简化为双线性。这使我能够计算KdV电荷的任何功率的期望值，然后找到这些期望值的模变换。现在我将开始看其他理论，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。一开始，我要看看能否计算出KdV电荷的期望值如果可能的话，我要试着找出这些期望值的模变换。最后的目的是为这些期望值找到一个通用的转换公式，看看是否有任何通用的特征可以跨越不同的理论。

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.