Non-renormalization theorem and cyclic Leibniz rule in lattice supersymmetry

TL;DR

This paper introduces a lattice model of supersymmetric quantum mechanics that employs a cyclic Leibniz rule to preserve some supersymmetry and demonstrates a non-renormalization theorem, mirroring continuum properties.

Contribution

The paper presents a novel lattice formulation using the cyclic Leibniz rule, enabling partial supersymmetry preservation and non-renormalization properties in lattice supersymmetric models.

Findings

CLR allows two supercharges to be preserved on the lattice.

No quantum corrections to potential terms at any finite order.

CLR is crucial for establishing the non-renormalization theorem.

Abstract

We propose a lattice model of supersymmetric complex quantum mechanics which realizes the non-renormalization theorem on a lattice. In our lattice model, the Leibniz rule in the continuum, which cannot hold on a lattice due to a no-go theorem, is replaced by the cyclic Leibniz rule (CLR) for difference operators. It is shown that CLR allows two of four supercharges of the continuum theory to preserve while a naive lattice model can realize one supercharge at the most. A striking feature of our lattice model is that there are no quantum corrections to potential terms in any finite order of perturbation theory. This is one of characteristic properties of supersymmetric theories in the continuum. It turns out that CLR plays a crucial role in the proof of the non-renormalization theorem. This result suggests that CLR grasps an essence of supersymmetry on a lattice.