Scale invariant behavior in a large N matrix model

TL;DR

This paper demonstrates scale invariance emergence in a large N matrix model of gauge theory with massless fermions, highlighting the transition from UV to IR behavior through eigenvalue distributions of Wilson loops.

Contribution

It provides numerical evidence of scale invariance in a matrix model representing an $SU(N)$ gauge theory with two massless adjoint fermions at large N.

Findings

Eigenvalue distributions indicate scale invariance at IR fixed point.

No universal beta-function connects UV and IR regimes.

Numerical methods reveal transition behavior in the matrix model.

Abstract

Eigenvalue distributions of properly regularized Wilson loop operators are used to study the transition from ultra-violet (UV) behavior to infra-red (IR) behavior in gauge theories coupled to matter that potentially have an IR fixed point (FP). We numerically demonstrate emergence of scale invariance in a matrix model that describes $SU(N)$ gauge theory coupled to two flavors of massless adjoint fermions in the large $N$ limit. The eigenvalue distribution of Wilson loops of varying sizes cannot be described by a universal lattice beta-function connecting the UV to the IR.