Running Coupling in pure gauge theories using the Schr\"odinger functional

TL;DR

This paper employs the Schr"odinger functional approach to define and compute a non-perturbative running coupling in pure SU(2) gauge theory across a broad range of length scales using lattice simulations.

Contribution

It introduces a non-perturbative method to calculate the running coupling in pure gauge theories via the Schr"odinger functional and lattice techniques.

Findings

Non-perturbative running coupling computed for a wide range of scales.

Continuum limit achieved through finite size scaling.

Results connect perturbative and non-perturbative regimes.

Abstract

Schr\"odinger functional, the propagation kernel for going from some field configuration at time $x^0=0$ to some other configuration at $x^0=T$, is used to define a running coupling, $\bar g^2(L)$, at a length scale, $L$, in pure gauge theories. Using a lattice formulation and finite size scaling techniques, this running coupling is calculated non-perturbatively in the continuum for a wide range of $L$, that extends from the perturbative scales to non-perturbative scales, for the specific case of pure SU(2) gauge theory.