Lorentzian dynamics and factorization beyond rationality

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 analyticity and 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.

Automated summary

The study investigates the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory and their effects on local operators. It delves into the factorization of local operators into holomorphic and anti-holomorphic defect operators connected by topological defect lines, and explores the implications for analyticity and Lorentzian dynamics, including aspects of chaos. The research also establishes a formula linking the infinite boost limit to the action of topological defect lines on local operators, with applications in understanding the opacity of bulk scattering.