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.
Highlights
Using ideas borrowed from topological field theory and orbifold constructions, a lattice formulation of N = 4 SYM has been developed which preserves a closed supersymmetry subalgebra at non-zero lattice spacing a > 0 [5,6,7]
We investigate the lattice regularization of 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
Summary
The mode number, which is the integrated eigenvalue density of the fermion operator, allows for a precise estimate of the mass anomalous dimension [28,29,30,31]. [28]) do not appear here This makes it possible to define a scale-dependent effective anomalous dimension from any two values of the mode number: γeff(Ω). The spectral density of D†D is obtained by mapping the interval [−1, 1] back to the original eigenvalue region [λ2min, λ2max], and can be integrated analytically to provide the mode number via eq (3.2). In addition to checking the stochastic results for small Ω, these direct eigenvalue measurements can provide an alternative estimate of the effective anomalous dimension, from the volume-scaling relation [12]. We will see below that the mode number provides more precise results than the individual eigenvalues, as expected [29, 30]
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