论文标题
liouville共形场理论的Virasoro结构和散射矩阵
The Virasoro structure and the scattering matrix for Liouville conformal field theory
论文作者
论文摘要
在这项工作中，我们在与liouville共形田间理论相关的规范希尔伯特空间中构建了Virasoro代数的代表。 Virasoro操作员的研究是通过引入与磁盘中定义的Holomorthic Vector场相关的新的马尔可夫动力学家族进行的。作为输出，我们表明，可以通过Virasoro代数的作用对Liouville共形场理论的哈密致力体进行对角线。这使得该理论的散射矩阵是对角线的，并且所谓的原代田地的家族（这是哈密顿量的特征向量）承认对整个复杂平面的分析扩展，如物理学文献中所指出。
In this work, we construct a representation of the Virasoro algebra in the canonical Hilbert space associated to Liouville conformal field theory. The study of the Virasoro operators is performed through the introduction of a new family of Markovian dynamics associated to holomorphic vector fields defined in the disk. As an output, we show that the Hamiltonian of Liouville conformal field theory can be diagonalized through the action of the Virasoro algebra. This enables to show that the scattering matrix of the theory is diagonal and that the family of the so-called primary fields (which are eigenvectors of the Hamiltonian) admits an analytic extension to the whole complex plane, as conjectured in the physics literature.
