Carving out OPE space and precise $O(2)$ model critical exponents

TL;DR

This paper introduces advanced numerical bootstrap techniques to precisely determine critical exponents and OPE coefficients in the 3d O(2) model, resolving longstanding discrepancies with experimental data.

Contribution

It develops a cutting surface algorithm for isolating conformal field theories and applies it to the 3d O(2) model, achieving more accurate critical exponents.

Findings

New precise scaling dimensions for 3d O(2) model

Improved agreement with Monte Carlo simulations

Sharpened discrepancy between theory and experiment

Abstract

We develop new tools for isolating CFTs using the numerical bootstrap. A "cutting surface" algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d $O(2)$ model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old $8\sigma$ discrepancy between theory and experiment.