The perturbative computation of the gradient flow coupling for the twisted Eguchi-Kawai model with the numerical stochastic perturbation theory

TL;DR

This paper computes the gradient flow coupling for the twisted Eguchi-Kawai model using numerical stochastic perturbation theory, analyzing its flow time dependence and lattice artifacts to connect lattice and dimensional regularization schemes.

Contribution

It provides the first perturbative calculation of the gradient flow coupling in the twisted Eguchi-Kawai model using numerical stochastic perturbation theory.

Findings

Perturbative coefficients of the gradient flow coupling are obtained.

Flow time dependence of the coupling is analyzed.

Lattice artifacts at large flow times are discussed.

Abstract

The gradient flow method is a renormalization scheme in which the gauge field is flowed by the diffusion equation. The gradient flow scheme has benefits that the observables composed of flowed gauge fields do not require further renormalization and do not depend on the regularization. From the independence of the regularization, this scheme allows us to relate the lattice regularization and the dimensional regularization such as the $\overline{\mathrm{MS}}$ scheme. We compute the gradient flow coupling for the twisted Eguchi--Kawai model using the numerical stochastic perturbation theory. In this presentation we show the results of the perturbative coefficients of the gradient flow coupling and its flow time dependence. We investigate the beta function from the flow time dependence and discuss the lattice artifacts in the large flow time in taking the large-$N$ limit.