Non-renormalization theorem in a lattice supersymmetric theory and the cyclic Leibniz rule

TL;DR

This paper formulates a lattice N=4 supersymmetric quantum mechanics model, demonstrating exact conservation of some supercharges via the cyclic Leibniz rule and establishing a non-renormalization theorem for certain terms.

Contribution

It introduces a lattice formulation preserving some supersymmetry using the cyclic Leibniz rule and proves non-renormalization of specific effective action terms.

Findings

Two supercharges are exactly conserved on the lattice.

Type-II terms, including mass and interaction terms, are non-renormalized.

Type-I terms, like kinetic terms, receive quantum corrections.

Abstract

N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two supercharges, among four, are exactly conserved with the help of the cyclic Leibniz rule without spoiling the locality. In use of the cohomological argument, any possible local terms of the effective action are classified into two categories which we call type-I and type-II, analogous to the D- and F-terms in the supersymmetric field theories. We prove non-renormalization theorem on the type-II terms which include mass and interaction terms with keeping a lattice constant finite, while type-I terms such as the kinetic terms have nontrivial quantum corrections.