# Bootstrability in Line-Defect CFT with Improved Truncation Methods

**Authors:** V. Niarchos, C. Papageorgakis, P. Richmond, A. G. Stapleton, M. Woolley  
**arXiv:** [2306.15730](https://arxiv.org/abs/2306.15730)  
**Date:** 2023-06-27  
**Summary page:** https://www.summarizepaper.com/fr/paper/2306.15730v1/

## Abstract

We study the conformal bootstrap of 1D CFTs on the straight Maldacena-Wilson line in 4D ${\cal N}=4$ 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 $(4\pi)^2$, 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.