Complete supersymmetry on the lattice and a No-Go theorem: A simulation with intact supersymmetries on the lattice

TL;DR

This paper presents a lattice formulation that preserves full supersymmetry in a nonperturbative simulation, demonstrating the realization of supersymmetry and correct continuum limit, while addressing the challenges of nonlocality and fermion doubling.

Contribution

It introduces a lattice approach that maintains complete supersymmetry and solves related issues like fermion doubling using nonlocal derivatives and interactions.

Findings

Full supersymmetry realized in lattice simulation

Correct continuum limit achieved

Nonlocal derivatives address supersymmetry breaking

Abstract

In this work a lattice formulation of a supersymmetric theory is proposed and tested that preserves the complete supersymmetry on the lattice. The results of a one-dimensional nonperturbative simulation show the realization of the full supersymmetry and the correct continuum limit of the theory. It is proven that the violation of supersymmetry due to the absence of the Leibniz rule on the lattice can be amended only with a nonlocal derivative and nonlocal interaction term. The fermion doubling problem is also discussed, which leads to another important source of supersymmetry breaking on the lattice. This problem is also solved with a nonlocal realization.