标题： 洛伦兹动力学与超越理性化的因子分解 显示英文标题

标题： Lorentzian Dynamics and Factorization Beyond Rationality

摘要： 我们研究了二维共形场论的共形雷杰极限中拓扑缺陷线的出现。我们解释了局部算符如何可以分解为通过拓扑缺陷线连接的全纯和反全纯缺陷算符，并讨论了这对洛伦兹动力学（包括混沌方面）的影响。我们推导了一个公式，将无限洛伦兹提升极限（该极限在全息上编码了散射的“不透明性”）与拓扑缺陷线对局部算符的作用联系起来。利用不透明度的酉界和融合系数的正性，我们证明了一大类拓扑缺陷线的谱半径由它们的环圈期望值给出。分解还给出了局部算符代数与缺陷算符代数以及融合范畴数据之间的关系公式。然后我们从缺陷的角度回顾了有理共形场论中的分解，并检查了无理理论。在 $c = 1$ 自由玻色子理论的orbifold分支上，我们找到了通过该分支分解扭曲场的拓扑缺陷线的统一描述；在无理点处，扭曲场通过表现出连续缺陷算符谱的“非紧致”拓扑缺陷线分解。在此过程中，我们开始发展一种表征非紧致拓扑缺陷线的形式主义。 显示英文摘要

摘要： 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.