A gauge invariant exact renormalization group II

TL;DR

This paper develops a gauge invariant, regularized renormalization group flow equation for pure SU(N) gauge theory, enabling non-perturbative, gauge-invariant calculations without gauge fixing, and demonstrates its effectiveness by computing the one-loop beta function.

Contribution

It introduces a novel gauge invariant flow equation for SU(N) gauge theories, utilizing covariant higher derivatives and supergauge embedding, and proves its finiteness and universality at one loop.

Findings

Finiteness of the method at one loop with external gauge fields

Successful computation of the one-loop beta function without gauge fixing

Discovery of a duality changing the sign of the squared coupling constant

Abstract

A manifestly gauge invariant and regularized renormalization group flow equation is constructed for pure SU(N) gauge theory in the large N limit. In this way we make precise and concrete the notion of a non-perturbative gauge invariant continuum Wilsonian effective action. Manifestly gauge invariant calculations may be performed, without gauge fixing, and receive a natural interpretation in terms of fluctuating Wilson loops. Regularization is achieved by covariant higher derivatives and by embedding in a spontaneously broken SU(N|N) supergauge theory; the resulting heavy fermionic vectors are Pauli-Villars fields. We prove the finiteness of this method to one loop and any number of external gauge fields. A duality is uncovered that changes the sign of the squared coupling constant. As a test of the basic formalism we compute the one loop beta function, for the first time without any gauge fixing, and prove its universality with respect to cutoff function.