Continuous renormalization group $\beta$ function from lattice simulations

TL;DR

This paper introduces a non-perturbative real-space renormalization group method based on the gradient flow to compute the continuous $eta$ function in lattice simulations, demonstrated on 2-flavor QCD.

Contribution

It proposes a novel continuous scale change approach that does not depend on perturbation theory, applicable at non-perturbative fixed points, and offers a new framework for studying strongly coupled systems.

Findings

Accurately computes the $eta$ function for 2-flavor QCD.

Lattice predictions closely match full analysis results.

Provides a non-perturbative, intuitive understanding of strongly coupled systems.

Abstract

We present a real-space renormalization group transformation with continuous scale change to calculate the continuous renormalization group $\beta$ function in non-perturbative lattice simulations. Our method is motivated by the connection between Wilsonian renormalization group and the gradient flow transformation. It does not rely on the perturbative definition of the renormalized coupling and is also valid at non-perturbative fixed points. Although our method requires an additional extrapolation compared to traditional step scaling calculations, it has several advantages which compensates for this extra step even when applied in the vicinity of the perturbative fixed point. We illustrate our approach by calculating the $\beta$ function of 2-flavor QCD and show that lattice predictions from individual lattice ensembles, even without the required continuum and finite volume extrapolations, can be very close to the result of the full analysis. Thus our method provides a non-perturbative framework and intuitive understanding into the structure of strongly coupled systems, in addition to being complementary to existing lattice determinations.