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

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 $R\lesssim 1/g$, 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 $R\gtrsim 1/g$ has to be systematically explored to conclude real asymptotic behavior in large distance.

13 pages, 5 figures, uses elsart.cls, the final version to appear in Phys. Lett. B

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• Vacuum energy of two-dimensional N=(2,2) super Yang-Mills theory
• Lattice formulation of 2D $\mathcal{N}=(2,2)$ SQCD based on the B model twist
• Lattice studies of supersymmetric gauge theories
• Exact Lattice Supersymmetry at the Quantum Level for $N=2$ Wess-Zumino Models in 1- and 2-Dimensions
• Anomaly and Sign problem in $\mathcal{N}=(2,2)$ SYM on Polyhedra : Numerical Analysis
• Supersymmetric Gauge Theory on the Graph
• Nonperturbative phase diagram of two-dimensional $\mathcal{N}=(2,2)$ super-Yang--Mills