O(a) Improvement of 2D N=(2,2) Lattice SYM Theory

TL;DR

This paper develops an O(a) improved lattice formulation of 2D N=(2,2) supersymmetric Yang-Mills theory that preserves supersymmetry and ensures correct continuum limit without fine tuning.

Contribution

It introduces a tree-level O(a) improvement respecting exact supersymmetry and proves measure invariance, enhancing numerical simulation accuracy for the theory.

Findings

Improved lattice action with exponential decay interactions.

Preservation of supersymmetry Q at the lattice level.

Invariance of the path-integral measure under Q-transformation.

Abstract

We perform a tree-level O(a) improvement of two-dimensional N=(2,2) supersymmetric Yang-Mills theory on the lattice, motivated by the fast convergence in numerical simulations. The improvement respects an exact supersymmetry Q which is needed for obtaining the correct continuum limit without a parameter fine tuning. The improved lattice action is given within a milder locality condition in which the interactions are decaying as the exponential of the distance on the lattice. We also prove that the path-integral measure is invariant under the improved Q-transformation.