The Analytic Bootstrap at Higher Loops
This event is part of the HET Seminar Series.
In this talk I will discuss recent developments in the analytic conformal bootstrap and their application to large classes of conformal field theories (CFTs). The analytic bootstrap has revealed that all higher dimensional CFTs contain a weakly coupled sector, corresponding to operators with large spin. Through the use of the CFT inversion formula , I will show how including non-perturbative effects in the large spin expansion improve analytic results for the Ising and O(2) vector model and can yield new predictions for OPE coefficients. From there, I will demonstrate how going to higher order in the large spin expansion is related to one-loop Witten diagrams in AdS. I will conclude by presenting new results for the conformal block decomposition of loop-level Witten diagrams and how identities derived from AdS/CFT can be applied to the study of generic CFTs.