Status  Confirmed 
Seminar Series  RENCTHEO 
Subjects  hepth 
Date  Thursday 19 December 2019 
Time  10:00 
Institute  IHP 
Seminar Room  Salle 314 
Speaker's Last Name  Mazac 
Speaker's First Name  Dalimil 
Speaker's Email Address  
Speaker's Institution  Stony Brook 
Title  Sphere packing, modular bootstrap and extremal functionals 
Abstract  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 spherepacking density. In 8 and 24 dimensions, this bound is sharp and leads to a solution of the spherepacking problem in these dimensions, as originally proved by Viazovska et al. 
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