# Osborn Equation and Irrelevant Operators

## TL;DR

This paper investigates the Osborn Equation with irrelevant operators, revealing the necessity of a metric beta-function for consistency and deriving modified Weyl anomalies.

## Contribution

It introduces a beta-function for the metric in the Osborn Equation framework when irrelevant operators are present, and calculates the resulting Weyl anomalies.

## Key findings

- Necessity of a metric beta-function for consistency
- Modified Weyl anomalies due to irrelevant operators
- Enhanced understanding of local renormalization group in this context

## Abstract

The structure of the Osborn ("Local Renormalization Group") Equation in the presence of integer dimensional irrelevant operators is studied. We argue that the consistency of the anomalous part of the generating functional requires a beta-function for the metric. The modified form of the Weyl anomalies is calculated.