论文标题
liouville理论中的共形性自举
Conformal bootstrap in Liouville Theory
论文作者
论文摘要
在批判现象的背景下，保形性自举假设是理论物理学中的一个有力思想，从而导致了壮观的预测。它假设根据其三点相关函数而言，构成了共形场理论的相关函数的显式表达。在本文中，我们在liouville理论的背景下给出了共形性自举假说的第一个数学证明，这是自理论物理学的八十年代以来研究的二维结合域理论，并由F. David和最后三位最后三位作者使用概率理论构建。该证明是基于通过对非紧凑型谎言组的谐波分析的相关自我伴随操作员的频谱分析来基于Virasoro代数最高权重模块的概率结构，但在无限的维度设置中。
The conformal bootstrap hypothesis is a powerful idea in theoretical physics which has led to spectacular predictions in the context of critical phenomena. It postulates an explicit expression for the correlation functions of a conformal field theory in terms of its 3-point correlation functions. In this paper we give the first mathematical proof of the conformal bootstrap hypothesis in the context of Liouville theory, a 2-dimensional conformal field theory studied since the eighties in theoretical physics and constructed recently by F. David and the three last authors using probability theory. The proof is based on a probabilistic construction of the Virasoro algebra highest weight modules through spectral analysis of an associated self adjoint operator akin to harmonic analysis on non compact Lie groups but in an infinite dimensional setup.
