Peculiarities in the Spectrum of the Adjoint Scalar Kinetic Operator in Yang-Mills Theory

TL;DR

This paper investigates the spectrum of the covariant Laplacian for scalar particles in the adjoint representation within Yang-Mills theory, revealing potential implications for the validity of perturbative approaches at small scales.

Contribution

It provides the first detailed analysis of the low-lying eigenmodes spectrum of the adjoint scalar kinetic operator in Yang-Mills theory, suggesting non-perturbative effects dominate even at small distances.

Findings

The gap between the lowest eigenvalue and the mobility edge tends to infinity in the continuum limit.

The scalar propagator's perturbative expression may be misleading at small distance scales.

A possible link between low-lying eigenmode density and multi-critical matrix models is identified.

Abstract

We study the spectrum of low-lying eigenmodes of the kinetic operator for scalar particles, in the color adjoint representation of Yang-Mills theory. The kinetic operator is the covariant Laplacian, plus a constant which serves to renormalize mass. In the pure gauge theory, our data indicates that the interval between the lowest eigenvalue and the mobility edge tends to infinity in the continuum limit. On these grounds, it is suggested that the perturbative expression for the scalar propagator may be misleading even at distance scales that are small compared to the confinement scale. We also measure the density of low-lying eigenmodes, and find a possible connection to multi-critical matrix models of order m=1.