Improving the five-point bootstrap

TL;DR

This paper introduces an efficient algorithm for computing five-point conformal blocks in any dimension, improving accuracy and speed, and applies it to study the 3D critical Ising model's correlators.

Contribution

The paper develops a new recursive and series acceleration method for five-point conformal blocks and demonstrates its application to the 3D Ising model's correlator analysis.

Findings

Enhanced computational efficiency for five-point conformal blocks.

More accurate OPE coefficients in the 3D Ising model.

Improved approximation of high-dimension operator contributions.

Abstract

We present a new algorithm for the numerical evaluation of five-point conformal blocks in $d$-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Pad\'e approximant to accelerate its convergence. We then study the $\langle\sigma\sigma\epsilon\sigma\sigma\rangle$ correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff $\Delta\leqslant \Delta_{\rm cutoff}$. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.