# Supersymmetric gradient flow in the Wess-Zumino model

## TL;DR

This paper introduces a supersymmetric gradient flow in the four-dimensional Wess-Zumino model, ensuring supersymmetry is preserved during the flow, and analyzes its behavior including damping oscillations for nonzero mass.

## Contribution

The paper constructs a supersymmetric gradient flow in the Wess-Zumino model using both component and superfield formalisms, demonstrating its supersymmetry preservation.

## Key findings

- Flow exhibits damping oscillation with flow time for nonzero mass
- Flow is constructed to commute with supersymmetry transformations
- On-shell flow equation is also discussed

## Abstract

We propose a supersymmetric gradient flow equation in the four-dimensional Wess-Zumino model. The flow is constructed in two ways. One is based on the off-shell component fields and the other is based on the superfield formalism, in which the same result is provided. The obtained flow is supersymmetric because the flow time derivative and the supersymmetry transformation commute with each other. Solving the equation, we find that it has a damping oscillation with the flow time for nonzero mass, which is different from the Yang-Mills flow. The on-shell flow equation is also discussed.