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

Abstract

Abstract In this paper we use lattice simulation to study four dimensional N $$ \mathcal{N} $$ = 4 super Yang-Mills (SYM) theory. We have focused on the three color theory on lattices of size 124 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 N $$ \mathcal{N} $$ = 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.

Keywords

• Lattice Quantum Field Theory
• Supersymmetric Gauge Theory
• Wilson
• ’t Hooft and Polyakov loops
• Algorithms and Theoretical Developments