刘维理论解析延拓的路径积分方法：束域
Path integral approach to analytic continuation of Liouville theory: the pencil region
摘要：
利用David，Kupiainen，Rhodes和Vargas [DKRV 16]基于高斯乘性混沌理论的概率方法，研究了Liouville共形域论的解析延拓问题.其核心思想是将随机分析技术应用于与高斯自由场相关的布朗运动。我们加强了文献[KRV 17]中的结果，并且能够在一个无限三角形区域（我们称之为铅笔区域）上对Liouville理论的解析延拓提供严格的证明.这与物理学文献[HMW 11]一致。沿着这条线，我们开发了新的工具和估计的高斯措施和刘维相关函数使用这种概率的方法。
英文摘要：
We study the problem of analytic continuation of Liouville Conformal Field Theory using the probabilistic approach of David, Kupiainen, Rhodes and Vargas [DKRV16] based on the theory of Gaussian Multiplicative Chaos. The key idea is to apply stochastic calculus techniques to some Brownian motions associated to the Gaussian Free Field. We strengthen the results in [KRV17] and are able to provide rigorous justification of analytic continuation of Liouville Theory in an infinite trianglar region, which we call the pencil region. This is in accordance with the physics literature [HMW11]. Along the lines, we develop new tools and estimates of Gaussian measures and Liouville correlation functions using this probabilistic approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
