|
Abstract |
I will prove a theorem about 2D CFTs: Every unitary 2D CFT must contain a non-trivial 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 four-point SL(2) conformal bootstrap. In the second part of the
talk, I will
discuss a surprising connection between modular bootstrap and the sphere-packing 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. |
