# Conformal invariance for Wilson actions

## TL;DR

This paper reformulates the realization of conformal invariance in Wilson actions within the exact renormalization group framework, emphasizing simplicity and transparency through a new method based on equation-of-motion operators.

## Contribution

It introduces a simplified, transparent reformulation of conformal invariance for Wilson actions using a method for continuous symmetries in the exact renormalization group.

## Key findings

- Derived equations showing invariance of Wilson actions under conformal transformations
- Established that conformal transformations form a closed algebra in this formalism
- Provided a self-contained presentation with comprehensive background

## Abstract

We discuss the realization of conformal invariance for Wilson actions using the formalism of the exact renormalization group. This subject has been studied extensively in the recent works of O. J. Rosten. The main purpose of this paper is to reformulate Rosten's formulas for conformal transformations using a method developed earlier for the realization of any continuous symmetry in the exact renormalization group formalism. The merit of the reformulation is simplicity and transparency via the consistent use of equation-of-motion operators. We derive equations that imply the invariance of the Wilson action under infinitesimal conformal transformations which are non-linearly realized but form a closed conformal algebra. The best effort has been made to make the paper self-contained; ample background on the formalism is provided.