Some physics of the two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory: Lattice Monte Carlo study

TL;DR

This study uses lattice Monte Carlo simulations to explore physical properties of two-dimensional $ abla=(2,2)$ supersymmetric SU(2) Yang-Mills theory, focusing on correlation functions and static potential behavior.

Contribution

It provides the first lattice Monte Carlo analysis of the confining potential and correlation functions in this specific supersymmetric gauge theory.

Findings

Power-like correlation functions indicate no mass gap.

Observed linear confining potential for small distances.

Potential screening behavior at larger distances remains to be confirmed.

Abstract

We illustrate some physical application of a lattice formulation of the two-dimensional $\mathcal{N}=(2,2)$ supersymmetric SU(2) Yang-Mills theory with a (small) supersymmetry breaking scalar mass. Two aspects, power-like behavior of certain correlation functions (which implies the absence of the mass gap) and the static potential $V(R)$ between probe charges in the fundamental representation, are considered. For the latter, for $R\lesssim1/g$, we observe a linear confining potential with a finite string tension. This confining behavior appears distinct from a theoretical conjecture that a probe charge in the fundamental representation is screened in two-dimensional gauge theory with an adjoint massless fermion, although the static potential for $R\gtrsim1/g$ has to be systematically explored to conclude real asymptotic behavior in large distance.