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 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.
Highlights
Two-dimensional conformal field theory enjoys special kinematics that lead to holomorphically factorized continuous symmetries [1]
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
The role of line defects in the bulk topological quantum field theory is replaced by topological defect lines (TDLs) of the conformal field theory, and a local operator can be regarded as the composite of a holomorphic and an anti-holomorphic defect operator connected by a topological defect line
Summary
Two-dimensional conformal field theory enjoys special kinematics that lead to holomorphically factorized continuous symmetries [1]. Regge limit [60, 61] at infinite boost is completely fixed by the action of the topological defect line on local operators For rational theories, this connection was explored from a bulk perspective by [62] in the context of out-of-time-ordered correlators and chaos.
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