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We investigate the lattice regularization of $\mathcal{N} = 4$ supersymmetricYang-Mills theory, by stochastically computing the eigenvalue mode number ofthe fermion operator. This provides important insight into the non-perturbativerenormalization group flow of the lattice theory, through the definition of ascale-dependent effective mass anomalous dimension. While this anomalousdimension is expected to vanish in the conformal continuum theory, the finitelattice volume and lattice spacing generically lead to non-zero values, whichwe 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 quantifyingthe increasing significance of lattice artifacts at larger couplings.

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