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

Understand

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.