Two-dimensional $\mathcal{N}=2$ Super-Yang-Mills Theory

TL;DR

This paper investigates the two-dimensional $ ext{N}=2$ Super-Yang-Mills theory derived from a higher-dimensional model, demonstrating how to restore supersymmetry in the continuum limit through lattice simulations and fine-tuning.

Contribution

It presents a lattice formulation of 2D $ ext{N}=2$ SYM that explicitly breaks supersymmetry but restores it in the continuum limit via fine-tuning of fermion masses.

Findings

Mass spectra indicate supersymmetry restoration.

Ward identities confirm supersymmetry in the continuum.

Explicit symmetry breaking is controlled and eliminated.

Abstract

Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the $\mathcal{N}=1$ Super-Yang-Mills (SYM) theory with gauge group SU(2) dimensionally reduced to two-dimensional $\mathcal{N}=2$ SYM theory. In our lattice formulation we break supersymmetry and chiral symmetry explicitly while preserving R symmetry. By fine tuning the bar-mass of the fermions in the Lagrangian we construct a supersymmetric continuum theory. To this aim we carefully investigate mass spectra and Ward identities, which both show a clear signal of supersymmetry restoration in the continuum limit.