Split Weyl transformations in quantum gravity

TL;DR

This paper explores different ways the Weyl group can be realized in quantum gravity with a cutoff, focusing on split gauge transformations to understand background dependence, extending previous work on scale transformations.

Contribution

It introduces a generalized framework for split Weyl transformations in quantum gravity, enhancing understanding of background dependence in the presence of a cutoff.

Findings

Generalizes previous work on scale transformations

Analyzes split gauge transformations in quantum gravity

Provides insights into background dependence

Abstract

We discuss various realizations of the Weyl group in the background field expansion of quantum gravity, in the presence of a cutoff, as required in applications of the functional renormalization group. In order to study the background--dependence, special attention is given to split gauge transformations, which act on the background field and fluctuation keeping the total metric unchanged. The results generalize previous works on global and local scale transformations.