Manifestly gauge invariant exact renormalization group
Manifestly gauge invariant exact renormalization group
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/\Lambda_{QCD}.
1-24
Arnone, Stefano
d2a9a0a5-34fd-4205-b5f4-107208f44fb2
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Rosten, Oliver J.
26ca1633-a7c7-418f-af0d-e65b4ec487ed
19 June 2006
Arnone, Stefano
d2a9a0a5-34fd-4205-b5f4-107208f44fb2
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Rosten, Oliver J.
26ca1633-a7c7-418f-af0d-e65b4ec487ed
Arnone, Stefano, Morris, Tim R. and Rosten, Oliver J.
(2006)
Manifestly gauge invariant exact renormalization group.
Pre-print, .
Abstract
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/\Lambda_{QCD}.
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Published date: 19 June 2006
Additional Information:
arXiv:hep-th/0606181v1
Identifiers
Local EPrints ID: 57006
URI: http://eprints.soton.ac.uk/id/eprint/57006
PURE UUID: 9989484c-f65b-481d-91ef-f91202d60215
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Date deposited: 13 Aug 2008
Last modified: 12 Dec 2021 02:36
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Contributors
Author:
Stefano Arnone
Author:
Oliver J. Rosten
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