Theory HEP Seminar

Sphere packing, quantum gravity and extremal functionals

Dalimil Mazáč

YITP
Stony Brook

Ultraviolet consistency of quantum gravitational theories requires the presence of new states at or below the Planck scale. In the setting of AdS3/CFT2, this statement follows from the modular bootstrap. It has been a long-standing problem to improve the best upper bound on the mass of the lightest non-graviton state in this context. I will explain how this can be done using the "analytic extremal functionals", which were originally developed for the four-point bootstrap in 1D. The new analytic upper bound on the dimension of the lightest nontrivial primary is c/8.503 at large c (central charge) -- an improvement over the previous best bound c/6 due to Hellerman.

I will also explain that the sphere packing problem of Euclidean geometry can be studied using a version of the modular bootstrap. The analytic functionals apply also in this context. They lead directly to the recent solution of the sphere-packing problem in 8 and 24 dimensions due to Viazovska and Cohn+Kumar+Miller+Radchenko+Viazovska. The talk will be based on arXiv:1905.01319.