Eigenvalue spectrum and scaling dimension of lattice $\mathcal{N} = 4$ supersymmetric Yang-Mills

TL;DR

This paper uses lattice simulations to study the eigenvalue spectrum of $ ext{N}=4$ supersymmetric Yang-Mills theory, revealing how lattice artifacts affect the effective mass anomalous dimension and its convergence to the continuum limit.

Contribution

It introduces a stochastic method to compute the eigenvalue mode number, providing new insights into the non-perturbative renormalization group flow of lattice $ ext{N}=4$ SYM.

Findings

Eigenvalue spectrum analysis confirms convergence to continuum results.

Lattice artifacts become more significant at larger couplings.

Finite volume effects influence the measured anomalous dimension.

Abstract

We investigate the lattice regularization of $\mathcal{N} = 4$ supersymmetric Yang-Mills theory, by stochastically computing the eigenvalue mode number of the fermion operator. This provides important insight into the non-perturbative renormalization group flow of the lattice theory, through the definition of a scale-dependent effective mass anomalous dimension. While this anomalous dimension is expected to vanish in the conformal continuum theory, the finite lattice volume and lattice spacing generically lead to non-zero values, which we use to study the approach to the continuum limit. Our numerical results, comparing multiple lattice volumes, 't Hooft couplings, and numbers of colors, confirm convergence towards the expected continuum result, while quantifying the increasing significance of lattice artifacts at larger couplings.