Lorentzian dynamics and factorization beyond rationality

Chang, Chi-Ming; Lin, Ying-Hsuan

doi:10.1007/jhep10(2021)125

Title: Lorentzian dynamics and factorization beyond rationality

Journal Article · 14 October 2021 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep10(2021)125 · OSTI ID:1833715

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Tsinghua Univ., Beijing (China); Beijing Institute of Mathematical Sciences and Applications (BIMSA) (China); Caltech
Harvard Univ., Cambridge, MA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

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.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); National Key R&D Program of China

Grant/Contract Number:: SC0011632

OSTI ID:: 1833715

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 10 Vol. 2021; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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