Manifestly Gauge Invariant Exact Renormalization Group
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We construct a manifestly gauge invariant Exact Renormalization Group for SU(N) Yang-Mills theory, in a form suitable for calculations without gauge fixing at any order of perturbation theory. The effective cutoff is incorporated via a manifestly realised spontaneously broken SU(N|N) gauge invariance. Diagrammatic methods are developed which allow the calculations to proceed without specifying the precise form of the cutoff structure. We confirm consistency by computing for the first time both the one and two loop beta function coefficients without fixing the gauge or specifying the details of the cutoff. We sketch how to incorporate quarks and thus compute in QCD. Finally we analyse the renormalization group behaviour as the renormalized coupling becomes large, and show that confinement is a consequence if and only if the coupling diverges in the limit that all modes are integrated out. We also investigate an expansion in the inverse square renormalized coupling, and show that under general assumptions it yields a new non-perturbative approximation scheme corresponding to expanding in 1/Λ_{QCD}.
24 pages, 14 figures, Fields Inst style file; Talk presented by TRM at RG2005, Helsinki, Finland, September 2005 and Renormalization and Universality in Mathematical Physics Workshop, Fields Institute, Toronto, Canada, October 2005, extended to include more details on the strong renormalized coupling expansion. To be publ. as proceedings by the Fields Institute
24 pages, 14 figures, Fields Inst style file; Talk presented by TRM at RG2005, Helsinki, Finland, September 2005 and Renormalization and Universality in Mathematical Physics Workshop, Fields Institute, Toronto, Canada, October 2005, extended to include more details on the strong renormalized coupling expansion. To be publ. as proceedings by the Fields Institute