An anisotropic hybrid non-perturbative formulation for 4D N = 2 supersymmetric Yang-Mills theories

TL;DR

This paper introduces a simplified, non-perturbative lattice formulation for 4D N=2 supersymmetric Yang-Mills theories, applicable to both non-commutative and commutative cases, facilitating computer simulations.

Contribution

It presents a new, simpler non-perturbative formulation combining deconstruction, momentum cut-off, and matrix model techniques, with a moduli fixing term preserving supersymmetry.

Findings

Formulation is more suitable for computer simulations.

Applicable to both non-commutative and commutative theories.

Potential as a non-perturbative tool for 4D N=2 SYM theories.

Abstract

We provide a simple non-perturbative formulation for non-commutative four-dimensional N = 2 supersymmetric Yang-Mills theories. The formulation is constructed by a combination of deconstruction (orbifold projection), momentum cut-off and matrix model techniques. We also propose a moduli fixing term that preserves lattice supersymmetry on the deconstruction formulation. Although the analogous formulation for four-dimensional N = 2 supersymmetric Yang-Mills theories is proposed also in Nucl.Phys.B857(2012), our action is simpler and better suited for computer simulations. Moreover, not only for the non-commutative theories, our formulation has a potential to be a non-perturbative tool also for the commutative four-dimensional N = 2 supersymmetric Yang-Mills theories.