Bootstrapping critical Ising model on three-dimensional real projective space

TL;DR

This paper develops a numerical bootstrap method to analyze the critical Ising model on a three-dimensional real projective space, providing precise estimates of one-point functions and demonstrating a new approach for conformal field theories on complex geometries.

Contribution

The authors introduce a bootstrap approach for conformal field theories on non-trivial geometries, specifically the real projective space, with high accuracy and convergence.

Findings

Rapid convergence of bootstrap in 2D verified against exact solutions

Estimated systematic error less than 1% for 3D critical Ising model

Method enables solving CFTs on complex geometries

Abstract

Given a conformal data on a flat Euclidean space, we use crosscap conformal bootstrap equations to numerically solve the Lee-Yang model as well as the critical Ising model on a three-dimensional real projective space. We check the rapid convergence of our bootstrap program in two-dimensions from the exact solutions available. Based on the comparison, we estimate that our systematic error on the numerically solved one-point functions of the critical Ising model on a three-dimensional real projective space is less than one percent. Our method opens up a novel way to solve conformal field theories on non-trivial geometries.