Numerical computation of the beta function of large N SU(N) gauge theory coupled to an adjoint Dirac fermion

TL;DR

This paper investigates the non-perturbative scaling behavior of large N SU(N) gauge theory with an adjoint Dirac fermion using lattice simulations, finding evidence of a near-zero beta function.

Contribution

It provides a numerical study of the beta function in large N gauge theory with adjoint fermions, highlighting slow scale variation and potential near-conformal behavior.

Findings

No perturbative scaling observed in studied region

Scale varies slowly with bare coupling

Eigenvalues suggest beta function approaches zero

Abstract

We use a single site lattice in four dimensions to study the scaling of large N Yang-Mills field coupled to a single massless Dirac fermion in the adjoint representation. We use the location of the strong to weak coupling transition defined through the eigenvalues of the folded Wilson loop operator to set a scale. We do not observe perturbative scaling in the region studied in this paper. Instead, we observe that the scale changes very slowly with the bare coupling. The lowest eigenvalue of the overlap Dirac operator is another scale that shows similar behavior as a function of the lattice coupling. We speculate that this behavior is due to the beta function appoaching close to a zero.