Upgrading Extremal Flows in the Space of Derivatives

TL;DR

This paper enhances the extremal flows method for solving bootstrap constraints, enabling higher-order solutions and revealing the complex structure of the solution space.

Contribution

It develops a generalized approach to extremal flows with discontinuities, improving solution accuracy in the spinning modular bootstrap.

Findings

Successfully upgrades solutions from low to high numerical order

Reveals the richness and complexity of the bootstrap solution space

Provides a prototype method applicable to broader bootstrap problems

Abstract

The method of extremal flows has presented an alluring alternative approach to numerically solving bootstrap constraints. Here I present the development and adaptation of that approach to a more general class of flows with apparent discontinuities. I focus on upgrading solutions of gap maximization for the spinning modular bootstrap from low to high numerical order, though the methodology is generic to a broader class of bootstrap constraints and flows. This methodology presents various nontrivialities and nuances which reflect a richness of the space of bootstrap solutions. The result is a prototype which successfully upgrades solutions in a simple test case at small scale.