Operator product expansion coefficients from the nonperturbative functional renormalization group

TL;DR

This paper employs the nonperturbative functional renormalization group to compute operator product expansion coefficients in various dimensions and universality classes, providing results consistent with known data and extending across a broad parameter range.

Contribution

It introduces a novel FRG-based method to calculate OPE coefficients in the O(N) and Ising universality classes across multiple dimensions.

Findings

FRG results agree with conformal bootstrap and Monte Carlo data where available.

Provides OPE coefficients for a range of dimensions and N values.

Extends calculations to dimensions and parameters lacking previous data.

Abstract

Using the nonperturbative functional renormalization group (FRG) within the Blaizot-M\'endez-Galain-Wschebor approximation, we compute the operator product expansion (OPE) coefficient $c_{112}$ associated with the operators $\mathcal{O}_1\sim\varphi$ and $\mathcal{O}_2\sim\varphi^2$ in the three-dimensional $\mathrm{O}(N)$ universality class and in the Ising universality class ($N=1$) in dimensions $2 \leq d \leq 4$. When available, exact results and estimates from the conformal bootstrap and Monte-Carlo simulations compare extremely well to our results, while FRG is able to provide values across the whole range of $d$ and $N$ considered.