Determination of the running coupling in pure SU(4) Yang-Mills theory

TL;DR

This paper uses the Schrödinger functional method to determine the running coupling in pure SU(4) Yang-Mills theory, connecting high-energy and low-energy regimes, and compares results across different N values to test large-N universality.

Contribution

It extends the Schrödinger functional approach to SU(4) and compares the running coupling with SU(2) and SU(3), testing large-N predictions and determining Lambda_SF in units of the string tension.

Findings

The running coupling is successfully determined across a wide energy range.

The large-N expectation that g^2*N is universal is supported down to low energies.

Lambda_SF/√σ is computed as a function of N at leading order in 1/N^2.

Abstract

The Schrodinger functional is used to define a renormalised coupling for pure SU(4) Yang-Mills theory, with Wilson action and suitably selected boundary conditions on the link field. The coupling, which runs with the size of the lattice, is then determined by a finite-size scaling technique through a large range of momenta, thereby allowing a connection to be made between the high energy regime and the low energy non-perturbative regime, where contact is made with the physical scale of the theory. Using data from previous SU(2) and SU(3) simulations obtained with the same technique, the running of the 't Hooft coupling defined through the Schrodinger functional is studied, and we check whether the large-N expectation that g^2*N is a universal function of the energy scale E holds down to energies of the order of the string tension. Finally, we determine Lambda_SF in units of the string tension as a function of N at leading order in 1/N^2.