Orateur
Description
We consider the implications of modular invariance for the spectrum of two-dimensional CFTs. For states with high energy this question was analyzed at a qualitative level by Cardy in 1986, but rigorous statements were almost entirely absent until the analysis (based on Tauberian theorems) by Mukhametzhanov and Zhiboedeov in 2019. In this talk we consider states with a very large spin, for which we show that it is possible to obtain much stronger rigorous results. Using complex analysis we in particular demonstrate that the spectrum of twists necessarily becomes dense for every large spin. We analyze the size of the subleading corrections, which will allow us to estimate how rapidly the maximal spacing between operators goes to zero. An entirely analogous procedure can be applied to four-point functions of identical operators in CFTs with a twist gap.
Talk based on work in progress with Sridip Pal and Jiaxin Qiao.
