The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT

TL;DR

This paper combines numerical and analytical methods to analyze the spectrum and operator product expansion data of the 3d O(2) critical model, confirming predictions and exploring Regge trajectories.

Contribution

It introduces a combined approach using the extremal functional method and Lorentzian inversion formula to study the 3d O(2) model's spectrum and OPE coefficients.

Findings

Agreement between analytical and numerical predictions.

Evidence for scalar operators on double-twist Regge trajectories.

Estimates of leading Regge intercepts for the O(2) model.

Abstract

We study the spectrum and OPE coefficients of the three-dimensional critical O(2) model, using four-point functions of the leading scalars with charges 0, 1, and 2 ($s$, $\phi$, and $t$). We obtain numerical predictions for low-twist OPE data in several charge sectors using the extremal functional method. We compare the results to analytical estimates using the Lorentzian inversion formula and a small amount of numerical input. We find agreement between the analytic and numerical predictions. We also give evidence that certain scalar operators lie on double-twist Regge trajectories and obtain estimates for the leading Regge intercepts of the O(2) model.