Results from lattice simulations of N=4 supersymmetric Yang--Mills

TL;DR

This paper presents lattice simulation results of N=4 supersymmetric Yang-Mills theory, demonstrating minimal fine-tuning, supersymmetry restoration, absence of sign problem, and Coulombic static potential consistent with perturbation theory.

Contribution

It provides new lattice evidence on supersymmetry restoration, sign problem absence, and static potential behavior in N=4 SYM, with extensions to N=3 colors.

Findings

Only one fine-tuning needed if moduli space isn't lifted.

Lattice theory shows no sign problem.

Static potential is Coulombic at various couplings.

Abstract

We report recent results and developments from our ongoing lattice studies of $\mathcal N = 4$ supersymmetric Yang--Mills theory. These include a proof that only a single fine-tuning needs to be performed, so long as the moduli space is not lifted by nonperturbative effects. We extend our investigations of supersymmetry restoration in the continuum limit by initiating Monte Carlo renormalization group studies. We present additional numerical evidence that the lattice theory does not suffer from a sign problem. Finally we study the static potential, which we find to be Coulombic at both weak and strong coupling. We compare the static potential Coulomb coefficients to perturbation theory, including initial results for N=3 colors in addition to N=2.