Nathan Benjamin of Princeton University will give the Stanford Institute for Theoretical Physics (SITP) Monday Colloquium.

**Abstract**

I will discuss the large spin spectrum of two-dimensional conformal field theories by looking at the modular bootstrap in the lightcone limit. In the presence of a twist gap amongst the Virasoro primary operators (where twist is the difference between conformal dimension and spin), there is a universal expression for the density of states that extends beyond the usual Cardy regime. This expression has an interesting feature which suggests a new upper bound on the lowest twist primary operator present in any 2d CFT. For theories holographically dual to large-radius gravity in AdS$_3$, this new bound is below the BTZ threshold, which in particular would imply that pure AdS$_3$ gravity does not exist.