Bootstrability in Line-Defect CFT with Improved Truncation Methods

Abstract

We study the conformal bootstrap of 1D CFTs on the straight Maldacena-Wilson line in 4D $\mathcal{N}=4$ super-Yang-Mills theory. We introduce an improved truncation scheme with an 'OPE tail' approximation and use it to reproduce the 'bootstrability' results of Cavaglià et al. for the OPE-coefficients squared of the first three unprotected operators. For example, for the first OPE-coefficient squared at 't Hooft coupling $(4\pi {)}^2$, linear-functional methods with two sum rules from integrated correlators give the rigorous result $0.294014873\pm 4.88\cdot 10^{-8}$, whereas our methods give with machine-precision computations $0.294014228\pm 6.77\cdot 10^{-7}$. For our numerical searches, we benchmark the Reinforcement Learning Soft Actor-Critic algorithm against an Interior Point Method algorithm (IPOPT) and comment on the merits of each algorithm.

44 pages, 4 figures; v2: typos corrected and references added