Statut  Confirmé 
Série  RENCTHEO 
Domaines  hepth 
Date  Jeudi 19 Décembre 2019 
Heure  10:00 
Institut  IHP 
Salle  Salle 314 
Nom de l'orateur  Mazac 
Prenom de l'orateur  Dalimil 
Addresse email de l'orateur  
Institution de l'orateur  Stony Brook 
Titre  Sphere packing, modular bootstrap and extremal functionals 
Résumé  I will prove a theorem about 2D CFTs: Every unitary 2D CFT must contain a nontrivial Virasoro primary of scaling dimension at most c/8 + 1/2, where c is the central charge. At large c, this is an improvement of the Hellerman bound c/6 + O(1), and is relevant for constraining the spectrum of gravitational theories in AdS3. The proof follows from the modular bootstrap and uses analytic extremal functionals, originally developed in the context of fourpoint SL(2) conformal bootstrap. In the second part of the talk, I will discuss a surprising connection between modular bootstrap and the spherepacking problem from discrete geometry. In particular, the above bound on the gap becomes a bound on the sphere packing density. In 8 and 24 dimensions, this bound is sharp and leads to a solution of the sphere packing problem in these dimensions, as originally proved by Viazovska et al. 
Numéro de preprint arXiv  
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