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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2025-06-01
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| Series: | Journal of High Energy Physics |
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| 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. |
| format | Article |
| id | doaj-art-deb52c8a5a7a4569a28bab20b8599019 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| 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 |