Novel Approach to Super Yang-Mills Theory on Lattice - Exact fermionic symmetry and "Ichimatsu" pattern -

TL;DR

This paper introduces a lattice formulation of Super Yang-Mills theory with an exact fermionic symmetry, utilizing a novel

Contribution

It proposes a new lattice model with an exact fermionic symmetry and a unique gauge action pattern, advancing the realization of supersymmetric theories on the lattice.

Findings

Fermionic symmetry persists in the continuum limit.

The gauge action uses a novel

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Abstract

We present a lattice theory with an exact fermionic symmetry, which mixes the link and the fermionic variables. The staggered fermionic variables may be reconstructed into a Majorana fermion in the continuum limit. The gauge action has a novel structure. Though it is the ordinary plaquette action, two different couplings are assigned in the ``Ichimatsu pattern'' or the checkered pattern. In the naive continuum limit, the fermionic symmetry survives as a continuum (or an $O(a^0)$) symmetry. The transformation of the fermion is proportional to the field strength multiplied by the difference of the two gauge couplings in this limit. This work is an extension of our recently proposed cell model toward the realization of supersymmetric Yang-Mills theory on lattice.