Two-Dimensional Compact N=(2,2) Lattice Super Yang-Mills Theory with Exact Supersymmetry

TL;DR

This paper develops a two-dimensional lattice super Yang-Mills theory with exact supersymmetry, using compact variables for gauge and Higgs fields, ensuring a well-defined path integral and correct continuum limit without fine-tuning.

Contribution

It introduces a novel lattice formulation of N=(2,2) super Yang-Mills with compact variables and exact supersymmetry, leading to a well-defined path integral and proper continuum behavior.

Findings

The model maintains one exact supercharge.

The gauge group is U(N) due to supersymmetry and compact fields.

The theory flows to the continuum limit without fine-tuning.

Abstract

We construct two-dimensional N=(2,2) lattice super Yang-Mills theory, where the gauge and Higgs fields are all represented by U(N) compact variables, with keeping one exact supercharge along the line of the papers [1,2,3]. Interestingly, requirements of the exact supersymmetry as well as of the compact gauge and Higgs fields lead to the gauge group U(N) rather than SU(N). As a result of the perturbative renormalization argument, the model is shown to flow to the target continuum theory without any fine-tuning. Different from the case of noncompact Higgs fields, the path integral along the flat directions is well-defined in this model.