Modular evolutions and causality in two-dimensional conformal field theory

Abstract In two-dimensional conformal field theories (CFT) in Minkowski spacetime, we study the spacetime distance between two events along two distinct modular trajectories. When the spatial line is bipartite by a single interval, we consider both the ground state and the state at finite different...

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Main Authors: Dobrica Jovanovic, Mihail Mintchev, Erik Tonni
Format: Article
Language:English
Published: SpringerOpen 2025-06-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP06(2025)185
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author Dobrica Jovanovic
Mihail Mintchev
Erik Tonni
author_facet Dobrica Jovanovic
Mihail Mintchev
Erik Tonni
author_sort Dobrica Jovanovic
collection DOAJ
description Abstract In two-dimensional conformal field theories (CFT) in Minkowski spacetime, we study the spacetime distance between two events along two distinct modular trajectories. When the spatial line is bipartite by a single interval, we consider both the ground state and the state at finite different temperatures for the left and right moving excitations. For the free massless Dirac field in the ground state, the bipartition of the line given by the union of two disjoint intervals is also investigated. The modular flows corresponding to connected subsystems preserve relativistic causality. Locality along the modular flows of some fields is explored by evaluating their (anti-)commutators. In particular, the bilocal nature of the modular Hamiltonian of two disjoint intervals for the massless Dirac field provide multiple trajectories leading to Dirac delta contributions in the (anti-)commutators even when the initial points belong to different intervals, thus being spacelike separated.
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institution Kabale University
issn 1029-8479
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series Journal of High Energy Physics
spelling doaj-art-deb52c8a5a7a4569a28bab20b85990192025-08-20T04:01:47ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025617210.1007/JHEP06(2025)185Modular evolutions and causality in two-dimensional conformal field theoryDobrica Jovanovic0Mihail Mintchev1Erik Tonni2Center for Theoretical Physics, Massachusetts Institute of TechnologyDipartimento di Fisica, Università di Pisa and IgNFN Sezione di PisaSISSA and INFN Sezione di TriesteAbstract In two-dimensional conformal field theories (CFT) in Minkowski spacetime, we study the spacetime distance between two events along two distinct modular trajectories. When the spatial line is bipartite by a single interval, we consider both the ground state and the state at finite different temperatures for the left and right moving excitations. For the free massless Dirac field in the ground state, the bipartition of the line given by the union of two disjoint intervals is also investigated. The modular flows corresponding to connected subsystems preserve relativistic causality. Locality along the modular flows of some fields is explored by evaluating their (anti-)commutators. In particular, the bilocal nature of the modular Hamiltonian of two disjoint intervals for the massless Dirac field provide multiple trajectories leading to Dirac delta contributions in the (anti-)commutators even when the initial points belong to different intervals, thus being spacelike separated.https://doi.org/10.1007/JHEP06(2025)185Field Theories in Lower DimensionsScale and Conformal Symmetries
spellingShingle Dobrica Jovanovic
Mihail Mintchev
Erik Tonni
Modular evolutions and causality in two-dimensional conformal field theory
Journal of High Energy Physics
Field Theories in Lower Dimensions
Scale and Conformal Symmetries
title Modular evolutions and causality in two-dimensional conformal field theory
title_full Modular evolutions and causality in two-dimensional conformal field theory
title_fullStr Modular evolutions and causality in two-dimensional conformal field theory
title_full_unstemmed Modular evolutions and causality in two-dimensional conformal field theory
title_short Modular evolutions and causality in two-dimensional conformal field theory
title_sort modular evolutions and causality in two dimensional conformal field theory
topic Field Theories in Lower Dimensions
Scale and Conformal Symmetries
url https://doi.org/10.1007/JHEP06(2025)185
work_keys_str_mv AT dobricajovanovic modularevolutionsandcausalityintwodimensionalconformalfieldtheory
AT mihailmintchev modularevolutionsandcausalityintwodimensionalconformalfieldtheory
AT eriktonni modularevolutionsandcausalityintwodimensionalconformalfieldtheory