Lattice Formulation of the N=4 D=3 Twisted Super Yang-Mills

TL;DR

This paper presents a lattice formulation for a three-dimensional super Yang-Mills model with twisted N=4 supersymmetry, fully realizing the supersymmetry algebra on the lattice through a modified Leibniz rule.

Contribution

It extends a gauge covariant lattice formulation to three dimensions, achieving exact realization of all eight supercharges with a geometric approach.

Findings

Supersymmetry algebra is exactly realized on the lattice.

The formulation employs link supercharges and shifted (anti-)commutators.

Discussion of potential solutions to critiques on the link formulation.

Abstract

A lattice formulation of a three dimensional super Yang-Mills model with a twisted N=4 supersymmetry is proposed. The extended supersymmetry algebra of all eight supercharges is fully and exactly realized on the lattice with a modified "Leibniz rule". The formulation we employ here is a three dimensional extension of the manifestly gauge covariant method which was developed in our previous proposal of Dirac-K\"ahler twisted N=2 super Yang-Mills on a two dimensional lattice. The twisted N=4 supersymmetry algebra is geometrically realized on a three dimensional lattice with link supercharges and the use of "shifted" (anti-)commutators. A possible solution to the recent critiques on the link formulation will be discussed.