Modular properties of algebraic structures arising from conformal field theory

共形场论产生的代数结构的模性质

• 批准号: 2554038
• 金额: --
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2554038
• 关键词: Modular; properties; algebraic; structures; arising

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.

目前我正在研究是否有可能找到不同 2d CFT 中守恒电荷的模变换公式。我从自由费米子理论开始，其中 KdV 电荷在费米子模式下简化为双线性。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。我现在将开始研究其他理论，从一些最小模型开始，看看是否可以在这些理论中确定 KdV 电荷的模变换。最初，我将看看是否可以计算 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。最终目标是找到这些期望值的通用变换公式，并看看是否存在跨不同理论的通用特征。