In this talk we explain the recent advance in finding structure constants using a combination of integrability and conformal bootstrap methods in 4D N=4 SYM. We obtain very sharp rigorous numerical bounds for the structure constant of the first nonprotected state, giving this observable with seven digits precision for the ’t Hooft coupling in the intermediate coupling region √ λ 4π ∼ 1, with the error decreasing quickly at large ’t Hooft coupling. Furthermore, we obtain 4-loop analytic results at weak coupling.

King’s College London