AI 中文总结
本研究针对中心电荷小于1的非有理共形场论虚刘维尔理论，建立了Ward恒等式与Belavin-Polyakov-Zamolodchikov微分方程，为共形自举程序的严格实现奠定了基础。
AI 中文摘要
虚刘维尔理论（Imaginary Liouville theory）近期被提出，作为中心电荷小于1的非有理共形场论（CFT）的路径积分构造（Usciati等人2026）。本研究在对虚高斯乘性混沌的拉普拉斯变换衰减性作出精确假设的前提下，在该框架下建立了Ward恒等式与Belavin-Polyakov-Zamolodchikov微分方程。这些结果为中心电荷低于1的共形场论的共形自举程序的严格实现迈出了第一步，也是首次在精确计算之外探究虚刘维尔理论的内在性质。
英文摘要
Imaginary Liouville theory was recently proposed as a path integral construction of a non-rational conformal field theory (CFT) with central charge less than one (Usciati et al. 2026). In the present work, we establish Ward identities and Belavin-Polyakov-Zamolodchikov differential equations in this framework, assuming a precise conjecture on the decay of the Laplace transform of Imaginary Gaussian multiplicative chaos. These results provide a first step towards a rigorous implementation of the conformal bootstrap program for conformal field theories with central charge lower than one. This work is the first to investigate the intrinsic properties of Imaginary Liouville theory beyond exact computations.
