Lorentzian dynamics and factorization beyond rationality

Chi-Ming Chang Yau Mathematical Sciences Center (YMSC), Tsinghua University, Beijing, 100084, China; Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing, 101408, China Ying-Hsuan Lin Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, U.S.A.; Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, U.S.A.

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.74021

Journal of High Energy Physics, 2021, (125), 2021.10
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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@inproceedings{chi-ming2021lorentzian,
  title={Lorentzian dynamics and factorization beyond rationality},
  author={Chi-Ming Chang, and Ying-Hsuan Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220702144042514302517},
  booktitle={Journal of High Energy Physics},
  volume={2021},
  number={125},
  year={2021},
}
Chi-Ming Chang, and Ying-Hsuan Lin. Lorentzian dynamics and factorization beyond rationality. 2021. Vol. 2021. In Journal of High Energy Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220702144042514302517.
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