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

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 less than or similar to 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 greater than or similar to 1/g has to be systematically explored to conclude real asymptotic behavior in large distance. (C) 2009 Elsevier B.V. All rights reserved.