Simulations of ${\cal N}=2$ super Yang-Mills theory in two dimensions

TL;DR

This paper reports on lattice simulations of two-dimensional ${ m N}=2$ super Yang-Mills theory, demonstrating the preservation of supersymmetry and gauge invariance, and analyzing key quantum properties such as Ward identities and the moduli space.

Contribution

It introduces a lattice formulation that maintains exact supersymmetry and gauge invariance, enabling detailed non-perturbative studies of ${ m N}=2$ super Yang-Mills theory in two dimensions.

Findings

Supersymmetric Ward identities are verified numerically.

The phase of the Pfaffian is analyzed in detail.

The structure of the quantum moduli space is characterized.

Abstract

We present results from lattice simulations of ${\cal N}=2$ super Yang-Mills theory in two dimensions. The lattice formulation we use was developed in \cite{2dpaper} and retains both gauge invariance and an exact (twisted) supersymmetry for any lattice spacing. Results for both U(2) and SU(2) gauge groups are given. We focus on supersymmetric Ward identities, the phase of the Pfaffian resulting from integration over the Grassmann fields and the nature of the quantum moduli space.