Cyclic Leibniz rule: a formulation of supersymmetry on lattice

TL;DR

This paper introduces the cyclic Leibniz rule (CLR), a new relation on lattice that enhances the construction of supersymmetric theories, enabling more SUSYs and Nicolai mappings, demonstrated through a quantum-mechanical model with mass degeneracy.

Contribution

It proposes the cyclic Leibniz rule (CLR) as a novel lattice relation that extends supersymmetry construction capabilities.

Findings

CLR enables more SUSYs and Nicolai mappings

Exact fermion-boson mass degeneracy demonstrated

Enhanced lattice SUSY formulations achieved

Abstract

For the purpose of constructing supersymmetric(SUSY) theories on lattice, we propose a new type relation on lattice -cyclic Leibniz rule(CLR)- which is slightly different from an ordinary Leibniz rule. Actually, we find that CLR can enlarge the number of SUSYs and construct more Nicolai mappings in a quantum-mechanical model. In this model, the exact mass degeneracy between fermion and boson is shown.