Operator product expansion coefficients from the nonperturbative functional renormalization group

Abstract

Using the nonperturbative functional renormalization group (FRG) within the Blaizot-Méndez-Galain-Wschebor approximation, we compute the operator product expansion (OPE) coefficient $c_{112}$ associated with the operators ${\mathcal{O}}_1\sim \phi$ and ${\mathcal{O}}_2\sim {\phi }^2$ in the three-dimensional $\mathrm{O}(N)$ universality class and in the Ising universality class ($N=1$) in dimensions $2\le d\le 4$. 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.

11 pages, 4 figures. Final version

References in corpus (13)

• Exact evolution equation for the effective potential
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• The critical exponents of the superfluid transition in He4
• Conformal Bootstrap in Mellin Space
• Monte Carlo study of an improved clock model in three dimensions
• High-precision estimate of the hydrodynamic radius for self-avoiding walks
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach
• Composite Operators in Asymptotic Safety
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• On the geometry of the theory space in the ERG formalism