Manifestly gauge invariant computations

TL;DR

This paper introduces a gauge invariant exact renormalization group method that allows for the computation of the effective action and physical quantities without gauge fixing or ghosts, demonstrated by calculating the one-loop SU(N) Yang-Mills beta function.

Contribution

It presents a novel gauge invariant approach to compute the effective action and beta function without gauge fixing or ghosts, applicable at finite N.

Findings

Successful computation of the one-loop SU(N) Yang-Mills beta function without gauge fixing.

Method is independent of covariantisation and cutoff profile choices.

Provides a streamlined procedure for gauge invariant calculations.

Abstract

Using a gauge invariant exact renormalization group, we show how to compute the effective action, and extract the physics, whilst manifestly preserving gauge invariance at each and every step. As an example we give an elegant computation of the one-loop SU(N) Yang-Mills beta function, for the first time at finite N without any gauge fixing or ghosts. It is also completely independent of the details put in by hand, e.g. the choice of covariantisation and the cutoff profile, and, therefore, guides us to a procedure for streamlined calculations.