Modular evolutions and causality in two-dimensional conformal field theory
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13130_2025_Article_26501.pdf
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Author(s)
Jovanovic, Dobrica
Mintchev, Mihail
Tonni, Erik
Date Issued
June 19, 2025
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Jovanovic, D., Mintchev, M. & Tonni, E. Modular evolutions and causality in two-dimensional conformal field theory. J. High Energ. Phys. 2025, 185 (2025).
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/JHEP06(2025)185
