N=(1,1) Super Yang-Mills on a (2+1) Dimensional Transverse Lattice with one Exact Supersymmetry

TL;DR

This paper develops a lattice formulation of 2+1 dimensional N=(1,1) Super Yang-Mills theory that preserves one supersymmetry exactly, enabling numerical analysis of bound states and winding phenomena.

Contribution

It introduces a transverse lattice approach that maintains one supersymmetry exactly and explores the Hamiltonian's supercharge structure and bound state properties.

Findings

Good convergence in bound state calculations

Relation between fermion and boson massless states

Winding states with inverse mass dependence

Abstract

We present a formulation of N=(1,1), Super Yang-Mills theory in 2+1 dimensions using a transverse lattice methods that exactly preserves one supersymmetry. First, using a Lagrangian approach we obtain a standard transverse lattice formulation of the Hamiltonian. We then show that the Hamiltonian also can be written discretely as the square of a supercharge and that this produces a different result. Problems associated with the discrete realization of the full supercharge algebra are discussed. Numerically we solve for the bound states of the theory in the large N_c approximation and we find good convergence. We show that the number of fermion and boson massless bound states are closely related. Also we find that this theory admits winding states in the transverse direction and that their masses vary inversely with the winding number.