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

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 »« less

Authors:

^[1];

^[2]

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

Publication Date:: 2021-10-15

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.

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                    Chang, Chi-Ming, & Lin, Ying-Hsuan. Lorentzian dynamics and factorization beyond rationality.  United States.  https://doi.org/10.1007/jhep10(2021)125

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                    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.

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@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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Title: Lorentzian dynamics and factorization beyond rationality

Abstract

Citation Formats

Tensor Categories with Fusion Rules of Self-Duality for Finite Abelian Groups journal, November 1998

Polynomial equations for rational conformal field theories journal, October 1988

Cardy algebras and sewing constraints, II journal, September 2014

Operator product expansion convergence in conformal field theory journal, November 2012

Causality constraints in conformal field theory journal, May 2016

Fractional statistics and the butterfly effect journal, August 2016

On rational points in CFT moduli spaces journal, April 2021

Defect Lines, Dualities and Generalised Orbifolds conference, January 2012

Conformal Regge theory journal, December 2012

TFT construction of RCFT correlators I: partition functions journal, December 2002

The many faces of Ocneanu cells journal, June 2001

Topological transition on the conformal manifold journal, August 2020

On finite symmetries and their gauging in two dimensions journal, March 2018

Quelques propriétés spectrales des opérateurs positifs journal, June 1987

Euclidean Quantum Electrodynamics journal, August 1959

Black holes and the butterfly effect journal, March 2014

Analyticity in spin in conformal theories journal, September 2017

Stringy effects in scrambling journal, May 2015

On the crossing relation in the presence of defects journal, April 2010

Bounding the space of holographic CFTs with chaos journal, October 2016

Current algebra and Wess-Zumino model in two dimensions journal, December 1984

More on supersymmetric and 2d analogs of the SYK model journal, August 2017

TFT construction of RCFT correlatorsIII: simple currents journal, August 2004

A generalization of the Perron–Frobenius theorem journal, July 2000

Boundary conditions in rational conformal field theories journal, March 2000

Conformal Invariance, Unitarity, and Critical Exponents in Two Dimensions journal, April 1984

Models for Gapped Boundaries and Domain Walls journal, June 2012

Light-ray operators in conformal field theory journal, November 2018

Boundary conformal field theory approach to the critical two-dimensional Ising model with a defect line journal, June 1997

Duality defect of the monster CFT journal, January 2021

Symmetries and strings of adjoint QCD2 journal, March 2021

A (dummy’s) guide to working with gapped boundaries via (fermion) condensation journal, February 2021

Remarks on the canonical quantization of the Chern-Simons-Witten theory journal, October 1989

Topological defects in CFT journal, October 2013

H. H. Schaefer, Banach Lattices and Positive Operators (Springer-Verlag, 1974), xi + 376 pp., DM 98.00, $42.70. journal, March 1977

CONFORMAL BOUNDARY CONDITIONS: and what they teach us conference, November 2011

Functoriality of the center of an algebra journal, November 2015

Vacuum amplitudes without twist fields for the ZN orbifold and correlation functions of twist fields for the Z2 orbifold journal, June 1987

Fusion rules and modular transformations in 2D conformal field theory journal, January 1988

Naturality in conformal field theory journal, January 1989

Effect of boundary conditions on the operator content of two-dimensional conformally invariant theories journal, October 1986

The Fusion Algebra of Bimodule Categories journal, July 2007

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Invertible defects and isomorphisms of rational CFTs
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Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory
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Orbifold completion of defect bicategories
journal, January 2016

Boundary Conditions in Conformal Field Theory
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A bound on chaos
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The virtue of defects in 4D gauge theories and 2D CFTs
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Fusion of conformal interfaces
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On the Euclidean Structure of Relativistic Field Theory
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Notes on scrambling in conformal field theory
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The conformal field theory of orbifolds
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TFT construction of RCFT correlators II: unoriented world sheets
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Topological defect lines and renormalization group flows in two dimensions
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Looking for a bulk point
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Classical and quantum conformal field theory
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Reflection and transmission for conformal defects
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Spinning constraints on chaotic large c CFTs
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Defect Lines in the Ising Model and Boundary States on Orbifolds
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C=1 conformal field theories on Riemann surfaces
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TFT construction of RCFT correlators IV:
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Interactions on orbifolds
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Duality and defects in rational conformal field theory
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Taming the conformal zoo
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Cardy Algebras and Sewing Constraints, I
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Infinite conformal symmetry in two-dimensional quantum field theory
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Critical Ising correlation functions in the plane and on the torus
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Generalised twisted partition functions
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Strings on orbifolds (II)
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Universal RCFT correlators from the holomorphic bootstrap
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Topological defects for the free boson CFT
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Quantum field theory and the Jones polynomial
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Kramers-Wannier Duality from Conformal Defects
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Remarks on the canonical quantization of the Chern-Simons-Witten theory
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Scrambling in two-dimensional conformal field theories with light and smeared operators
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Fusion of conformal interfaces
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TFT construction of RCFT correlators IV: Structure constants and correlation functions
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