Perturbative analysis of the Wess-Zumino flow

TL;DR

This paper demonstrates that in the Wess-Zumino model, the supersymmetric gradient flow leads to ultraviolet finite correlators of flowed fields at all perturbation orders, offering insights distinct from gauge theories.

Contribution

It provides a perturbative analysis showing the ultraviolet finiteness of flowed field correlators in the Wess-Zumino model, leveraging nonrenormalization and initial conditions.

Findings

Correlators of flowed fields are ultraviolet finite at all orders.

The finiteness mechanism differs from gauge theories due to lack of gauge symmetry.

The approach enhances understanding of the gradient flow in supersymmetric models.

Abstract

We investigate an interacting supersymmetric gradient flow in the Wess-Zumino model. Thanks to the nonrenormalization 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 one-particle irreducible 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.