Some physics of the two-dimensional [formula omitted] supersymmetric Yang–Mills theory: Lattice Monte Carlo study

Issaku Kanamori,Hiroshi Suzuki

doi:10.1016/j.physletb.2009.01.039

Abstract

We illustrate some physical application of a lattice formulation of the two-dimensional 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≲1/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≳1/g has to be systematically explored to conclude real asymptotic behavior in large distance.

Highlights

Through the observation of a “partially conserved supercurrent relation”, we obtained [1] an affirmative numerical evidence that a lattice formulation in Ref. [2] provides a supersymmetric regularization of the two-Preprint submitted to Elsevier dimensional N = (2, 2) supersymmetric Yang-Mills theory (SYM) 1 2 S = 1 g2 d2x tr FM N + ΨT CΓM DM Ψ H2 (1)
The scalar mass term was added to suppress a possible large amplitude of scalar fields along flat directions that may amplify O(a) lattice artifacts to O(1) [1]
In the present Letter, we illustrate some physical application of this lattice formulation for the system S + Smass

Summary

Introduction

Through the observation of a “partially conserved supercurrent relation”, we obtained [1] an affirmative numerical evidence that a lattice formulation in Ref. [2] provides a supersymmetric regularization of the two-. Through the observation of a “partially conserved supercurrent relation”, we obtained [1] an affirmative numerical evidence that a lattice formulation in Ref. [2] provides a supersymmetric regularization of the two-. Preprint submitted to Elsevier dimensional N = (2, 2) supersymmetric Yang-Mills theory (SYM) 1 2. The scalar mass term was added to suppress a possible large amplitude of scalar fields along flat directions that may amplify O(a) lattice artifacts to O(1) [1]. In the present Letter, we illustrate some physical application of this lattice formulation for the system S + Smass

Correlation functions with power-like behavior

Potential energy between probe charges in the fundamental representation

Conclusion