论文标题
洛伦兹的动力和分解超出理性
Lorentzian Dynamics and Factorization Beyond Rationality
论文作者
论文摘要
我们研究了二维形成共形场理论的保形regge极限中拓扑缺陷线的出现。我们解释了如何通过拓扑缺陷线连接的尸体形态和抗孢子型缺陷操作员将本地操作员分解为对洛伦兹动态的含义，包括混乱的各个方面。我们得出了一个与无限增强极限相关的公式，该公式将全息编码散装散射的“不透明度”与拓扑缺陷线对本地操作员的作用。利用融合系数的不透明度和阳性的统一结合时，我们表明，大量拓扑缺陷线的光谱半径是由它们的循环期望值给出的。分解还提供了一个有关局部和缺陷操作员代数以及融合分类数据的公式。然后，我们从缺陷的角度回顾了理性保形场理论中的分解，并检查了非理性理论。在$ C = 1 $ Free Boson理论的Orbifold分支上，我们找到了拓扑缺陷线的统一描述，通过该描述将扭曲场分解为分解；在非理性点，扭曲场通过表现出连续缺陷操作员光谱的“非紧密肌力”拓扑缺陷线进行分解。在此过程中，我们启动形式主义的发展来表征非压缩拓扑缺陷线。
We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on Lorentzian dynamics including aspects of chaos. We derive a formula relating the infinite boost limit, which holographically encodes the "opacity" of bulk scattering, to the action of topological defect lines on local operators. Leveraging the unitary bound on the opacity and the positivity of fusion coefficients, we show that the spectral radii of a large class of topological defect lines are given by their loop expectation values. Factorization also gives a formula relating the local and defect operator algebras, and fusion categorical data. We then review factorization in rational conformal field theory from a defect perspective, and examine irrational theories. On the orbifold branch of the $c = 1$ free boson theory, we find a unified description for the topological defect lines through which the twist fields are factorized; at irrational points, the twist fields factorize through "non-compact" topological defect lines which exhibit continuous defect operator spectra. Along the way, we initiate the development of a formalism to characterize non-compact topological defect lines.
