# High Energy Theory Seminar

*,*Simons Center

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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 https://arxiv.org/pdf/1905.01319.pdf.