Summary of Super Doubler Approach on Exact Lattice Supersymmetry

TL;DR

This paper introduces a nonlocal lattice supersymmetry formulation called super doubler approach, which preserves exact supersymmetry and addresses chiral fermion issues, with potential applications to super Yang-Mills theory.

Contribution

It proposes a novel nonlocal lattice SUSY approach that maintains exact symmetry and overcomes chiral fermion problems, extending to super Yang-Mills theory.

Findings

Super doubler approach preserves exact SUSY on the lattice.

Modified approach recovers associativity and applies to super Yang-Mills.

Formulation is essentially equivalent to continuum theory, maintaining symmetry at finite lattice spacing.

Abstract

We have proposed a lattice SUSY formulation which we may call super doubler approach, where chiral fermion species doublers and their bosonic counter parts are either identified as super partners or truncated by chiral conditions. We claim that the super symmetry is exactly kept on the lattice. However the formulation is nonlocal and breaks lattice translational invariance. We argue that these features cause no fundamental difficulties in the continuum limit. Although a naive version of this formulation breaks associativity of the product of fields we have found a modified super doubler approach that recovers the associativity and is applicable to super Yang-Mills theory. It turns out that this formulation is essentially equivalent to the continuum formulation and thus keeps all the symmetry exact even at a finite lattice constant. Inspired by this formulation we propose a non-local lattice field theory formulation which is free of chiral fermion problem and has the same exact lattice symmetry as continuum theory.