In this talk, I will present an effective solution of the 1D crossing equation of 4 identical scalars. 1D CFTs provide universal constraints, the most general arising from a single correlator. Even though, little is known about the space of 1D unitary CFTs. Using appropriate bases of functionals, it is possible to write the crossing equation as a set of sum rules dual to solutions that saturate positivity bounds on the space of CFTs. In this context, we call them « extremal solutions ». I will present extremal solutions and how to reconstruct their entire CFT data using a hybrid method that combines both analytics and numerics. I will show evidence that in some precise limits, such solutions naturally describe flat space limit of QFTs in AdS2, allowing us to bootstrap their data in terms of 2d S-matrices and vice-versa. Finally, I will present how to reconstruct bulk AdS2 operators associated to extremal solutions. »

Noé Suchel / ENS Paris