Holography from lattice $$ \mathcal{N} $$ = 4 super Yang-Mills

In this paper we use lattice simulation to study four dimensional $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM) theory. We have focused on the three color theory on lattices of size 12 4 and for ’t Hooft couplings up to λ = 40 . 0. Our lattice action is based on a discretization of the Marcus or GL twist of $$ \mathcal{N} $$ N = 4 SYM and retains one exact supersymmetry for non-zero lattice spacing. We show that lattice theory exists in a single non-Abelian Coulomb phase for all ’t Hooft couplings. Furthermore the static potential we obtain from correlators of Polyakov lines is in good agreement with that obtained from holography — specifically the potential has a Coulombic form with a coefficent that varies as the square root of the ’t Hooft coupling.