Statut  Confirmé 
Série  PTIHES 
Domaines  hepth 
Date  Mercredi 20 Mars 2019 
Heure  14:00 
Institut  IHES 
Salle  Amphithéâtre Léon Motchane 
Nom de l'orateur  Hollands 
Prenom de l'orateur  Stefan 
Addresse email de l'orateur  
Institution de l'orateur  Univ. Leipzig 
Titre  Modular Flows in Quantum Field Theory 
Résumé  The reduced density matrix of a subsystem induces an intrinsic internal dynamics called the ``modular flow''. The flow depends on the subsystem and the given state of the total system. It has been subject to much attention in theoretical physics in recent times because it is closely related to information theoretic aspects of quantum field theory. In mathematics, the flow has played an important role in the study of operator algebras through the work of Connes and others. It is known that the flow has a geometric nature (boosts resp. special conformal transformations) in case the subsystem is defined by a spacetime region with a simple shape. For more complicated regions, important progress was recently made by Casini et al. who were able to determine the flow for multicomponent regions for free massless fermions or bosons in 1+1 dimensions. In this introductory lecture, I describe the physical and mathematical backgrounds underlying this research area. Then I describe a new approach which is not limited to free theories, based in an essential way on two principles: The socalled ``KMScondition'' and the exchange relations between primaries (braid relations) in rational CFTs in 1+1 dimensions. A combination of these ideas and methods from operator algebras establish that finding the modular flow of a multicomponent region is equivalent to a certain matrix RiemannHilbert problem. One can therefore apply known methods for this classic problem to find or at least characterize the modular flow. 
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