Bootstrability for 1d defect CFT

Abstract

In this talk I will describe the “bootstrability” program, which combines integrability techniques in 4d N = 4 SYM and the conformal bootstrap to study beyond-the-spectrum observables in a CFT.

I will start with a review of the quantum spectral curve (QSC), a powerful integrability based method to compute the non-perturbative planar spectrum of N = 4 SYM. Then I will show how it is modified to capture the spectrum of operator insertions on a 1/2-BPS Maldacena-Wilson line in the theory, thus solving the spectral problem of the associated defect CFT.

Finally, I will show how the boostrability approach allows us to access previously unreachable quantities such as correlation functions at finite coupling — we used this method to compute with good precision a non-supersymmetric structure constant for a wide range of the 't Hooft coupling in the defect CFT.