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

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 ($s$, $\ddot{I}•$, 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.

85 pages, 34 figures, 8 tables, Mathematica file attached. v2: Typos corrected, added footnote on small z expansion