# Derivation of a Gradient Flow from ERG

## TL;DR

This paper demonstrates a direct connection between gradient flow and renormalization group flow in scalar field theories using the exact RG formalism with a specific cutoff function.

## Contribution

It establishes a concrete correspondence between gradient flow and RG flow, providing a new perspective on their relationship in scalar field theories.

## Key findings

- Derived a formal link between gradient flow and RG flow.
- Used a specific cutoff function in the exact RG formalism.
- Provides a framework for understanding RG in terms of gradient flow.

## Abstract

We establish a concrete correspondence between a gradient flow and the renormalization group flow for a generic scalar field theory. We use the exact renormalization group formalism with a particular choice of the cutoff function.