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Title: Lorentzian dynamics and factorization beyond rationality

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 themore » development of a formalism to characterize non-compact topological defect lines.« less

Authors:
ORCiD logo [1]; ORCiD logo [2]
  1. Tsinghua Univ., Beijing (China); Beijing Institute of Mathematical Sciences and Applications (BIMSA) (China)
  2. Harvard Univ., Cambridge, MA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Key Research and Development Program of China
OSTI Identifier:
1833715
Grant/Contract Number:  
SC0011632; 2020YFA0713000
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2021; Journal Issue: 10; Journal ID: ISSN 1029-8479
Publisher:
Springer Nature
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Anomalies in Field and String Theories; Anyons; Conformal Field Theory; Field Theories in Lower Dimensions

Citation Formats

Chang, Chi-Ming, and Lin, Ying-Hsuan. Lorentzian dynamics and factorization beyond rationality. United States: N. p., 2021. Web. doi:10.1007/jhep10(2021)125.
Chang, Chi-Ming, & Lin, Ying-Hsuan. Lorentzian dynamics and factorization beyond rationality. United States. https://doi.org/10.1007/jhep10(2021)125
Chang, Chi-Ming, and Lin, Ying-Hsuan. Fri . "Lorentzian dynamics and factorization beyond rationality". United States. https://doi.org/10.1007/jhep10(2021)125. https://www.osti.gov/servlets/purl/1833715.
@article{osti_1833715,
title = {Lorentzian dynamics and factorization beyond rationality},
author = {Chang, Chi-Ming and Lin, Ying-Hsuan},
abstractNote = {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.},
doi = {10.1007/jhep10(2021)125},
journal = {Journal of High Energy Physics (Online)},
number = 10,
volume = 2021,
place = {United States},
year = {2021},
month = {10}
}

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