Bootstrability in line-defect CFTs with improved truncation methods
Vasilis Niarchos, Constantinos Papageorgakis, Paul Richmond, Alexander G. Stapleton, M. J. Woolley
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 Cavagli\`a 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 $(4\ensuremath{\pi}{)}^{2}$, linear-functional methods with two sum rules from integrated correlators give the rigorous result $0.294014873\ifmmode\pm\else\textpm\fi{}4.88\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, whereas our methods give with machine-precision computations $0.294014228\ifmmode\pm\else\textpm\fi{}6.77\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$. 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.