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We propose a lattice model of supersymmetric complex quantum mechanics whichrealizes 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 ano-go theorem, is replaced by the cyclic Leibniz rule (CLR) for differenceoperators. It is shown that CLR allows two of four supercharges of thecontinuum theory to preserve while a naive lattice model can realize onesupercharge at the most. A striking feature of our lattice model is that thereare no quantum corrections to potential terms in any finite order ofperturbation theory. This is one of characteristic properties of supersymmetrictheories in the continuum. It turns out that CLR plays a crucial role in theproof of the non-renormalization theorem. This result suggests that CLR graspsan essence of supersymmetry on a lattice.

Non-renormalization theorem and cyclic Leibniz rule in lattice supersymmetry