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, ϕ, 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.
Highlights
The conformal bootstrap is a powerful tool for exploring the space of conformal field theories
We compare the results to analytical estimates using the Lorentzian inversion formula and a small amount of numerical input
We describe how to apply the Lorentzian inversion formula to estimate low-twist OPE data
Summary
The conformal bootstrap is a powerful tool for exploring the space of conformal field theories. We use the numerical data provided in [5] and the extremal functional method [12, 18, 19] to obtain detailed numerical approximations for dimensions and OPE coefficients of low twist operators. Some byproducts of our study include a more detailed analysis of the O(2) representation theory and crossing equations, some computations of the Mean Field Theory (MFT) OPE coefficients in different O(2) charge sectors, a study of different expansions for 3d conformal blocks, new results for sums of SL2 blocks, and the introduction of a new concept, the sharing effect, which must be overcome for precise spectrum extraction in the numerical bootstrap. We will use the 20 allowed (primal) points given, with the parameters and gap assumptions given in tables 2 and 3, to compute both upper and lower bounds on the OPE coefficient fφφs. Λ keptPoleOrder order spins precision dualityGapThreshold primalErrorThreshold dualErrorThreshold initialMatrixScalePrimal initialMatrixScaleDual feasibleCenteringParameter infeasibleCenteringParameter stepLengthReduction maxComplementarity Threshold for spectrum.py
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