Properties of a proposed background independent exact renormalization group

TL;DR

This paper investigates a background independent exact renormalization group approach for gauge theories and gravity, highlighting its advantages and limitations, especially in the context of SU(N) Yang-Mills theory.

Contribution

It develops the machinery for analyzing a novel background independent RG approach and identifies fundamental limitations in regularization and gauge invariance preservation.

Findings

The approach preserves gauge invariance manifestly.

It does not fully regularize the longitudinal part of vertex functions at one loop.

A no-go theorem shows the two-point vertex flow cannot be both transverse and fully regularized.

Abstract

We explore the properties of a recently proposed background independent exact renormalization group approach to gauge theories and gravity. In the process we also develop the machinery needed to study it rigorously. The proposal comes with some advantages. It preserves gauge invariance manifestly, avoids introducing unphysical fields, such as ghosts and Pauli-Villars fields, and does not require gauge-fixing. However, we show that in the simple case of SU(N) Yang-Mills it does not completely regularise the longitudinal part of vertex functions already at one loop, invalidating certain methods for extracting universal components. Moreover we demonstrate a kind of no-go theorem: within the proposed structure, whatever choice is made for covariantisation and cutoff profiles, the two-point vertex flow equation at one loop cannot be both transverse, as required by gauge invariance, and fully regularised.