A Euclidean Lattice Construction of Supersymmetric Yang-Mills Theories with Sixteen Supercharges

TL;DR

This paper develops a lattice formulation for supersymmetric Yang-Mills theories with sixteen supercharges across various dimensions, enabling non-perturbative studies of these theories.

Contribution

It introduces a Euclidean lattice construction that preserves supersymmetry in the continuum limit for multiple dimensions, including N=4 in four dimensions.

Findings

Constructed supersymmetric lattice models for d=1,2,3,4

Achieved classical continuum limits matching supersymmetric Yang-Mills theories

Provided a Euclidean path integral formulation for Matrix Theory

Abstract

We formulate supersymmetric Euclidean spacetime Ad* lattices whose classical continuum limits are U(N) supersymmetric Yang-Mills theories with sixteen supercharges in d=1,2,3 and 4 dimensions. This family includes the especially interesting N=4 supersymmetry in four dimensions, as well as a Euclidean path integral formulation of Matrix Theory on a one dimensional lattice.