Lorentzian Dynamics and Factorization Beyond Rationality

TL;DR

This paper explores how topological defect lines influence Lorentzian dynamics and factorization in 2D conformal field theories, revealing new connections between defect operators, chaos, and spectral properties, especially in irrational theories.

Contribution

It introduces a formalism for non-compact topological defect lines and relates defect operator spectra to fusion data, extending factorization concepts beyond rational CFTs.

Findings

Spectral radii of defect lines equal their loop expectation values.

Factorization formulas connect local and defect operator algebras.

Unified description of defect lines in orbifold and irrational theories.

Abstract

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.