We investigate an interacting supersymmetric gradient flow in the Wess-Zumino
model. Thanks to the non-renormalization theorem and an appropriate initial
condition, we find that any correlator of flowed fields is ultraviolet finite.
This is shown at all orders of the perturbation theory using the power counting
theorem for 1PI supergraphs. Since the model does not have the gauge symmetry,
the mechanism of realizing the ultraviolet finiteness is quite different from
that of the Yang-Mills flow, and this could provide further understanding of
the gradient flow approach.Comment: 30 pages, 2 figure