Numerical Methods in the Conformal Bootstrap

TL;DR

This paper introduces accessible numerical techniques for the conformal bootstrap, including linear programming and modular invariance, making the field more approachable for newcomers and demonstrating practical bounds and methods.

Contribution

It provides a beginner-friendly overview of numerical bootstrap methods, including linear programming, extremal functionals, determinants, and modular bootstrap applications.

Findings

Basic bounds obtained via linear programming in Mathematica

Exploration of extremal functional and determinant methods

Initial steps towards modular invariance and crossing symmetry equations

Abstract

We present a low entry-level introduction to the Conformal Bootstrap. We review and obtain several basic bounds using Linear Programming in machine precision in Mathematica, making the results accessible even to the most uneducated computer user. The Extremal Functional Method and the method of determinants are also explored. Finally, we make an attempt at writing modular invariance statements as crossing symmetry equations for twist operators and perform Modular Bootstrap using 4-pt correlators.