Efficient Conformal Block Evaluation with GoBlocks

TL;DR

The paper introduces GoBlocks, a fast, parallel conformal block generator in Go, improving efficiency for bootstrap computations, especially in 3D Ising models, with significant speed gains over existing tools.

Contribution

We develop GoBlocks, a novel Go-based conformal block generator supporting multi-point and derivative evaluations, optimized for speed and moderate accuracy in bootstrap applications.

Findings

GoBlocks outperforms scalar_blocks in speed for moderate accuracy tasks.

Application to 3D Ising model bootstrap demonstrates practical efficiency.

Scalability analysis for larger O(N) models included.

Abstract

Conformal blocks in odd spacetime dimensions are not known in closed analytic form. To facilitate efficient computations in the conformal bootstrap, we introduce $\texttt{GoBlocks}$: a novel conformal-block generator implemented in the Go programming language, designed for rapid, on-the-fly, parallel evaluation using recursive relations. The package supports both multi-point and derivative-based bootstrap approaches and allows flexible control over accuracy and performance. We benchmark $\texttt{GoBlocks}$ against the $\texttt{scalar_blocks}$ package, finding significant speed improvements in applications where computational speed and moderate accuracy are critical, but ultra-high precision is not essential. As an illustration, we apply $\texttt{GoBlocks}$ to the mixed-correlator bootstrap of the three-dimensional Ising model, formulated as a non-convex optimisation problem in a suitable truncation scheme. We simultaneously optimise over external scaling dimensions and OPE CFT data. In addition, we discuss how the approach scales as we increase the number of mixed correlators in more general $O(N)$ vector models.