Gauge invariant regularisation via SU(N|N)

We construct a gauge invariant regularisation scheme for pure SU(N) Yang-Mills theory in fixed dimension four or less (for N = infinity in all dimensions), with a physical cutoff scale Lambda, by using covariant higher derivatives and spontaneously broken SU(N|N) supergauge invariance. Providing the...

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Bibliographic Details
Published in:arXiv.org 2001-11
Main Authors: Arnone, Stefano, Kubyshin, Yuri A, Morris, Tim R, Tighe, John F
Format: Article
Language:English
Subjects:
Derivatives
Divergence
Gauge invariance
Graphs
Infinity
Invariance
Invariants
Perturbation theory
Regularization
Yang-Mills theory
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Summary:We construct a gauge invariant regularisation scheme for pure SU(N) Yang-Mills theory in fixed dimension four or less (for N = infinity in all dimensions), with a physical cutoff scale Lambda, by using covariant higher derivatives and spontaneously broken SU(N|N) supergauge invariance. Providing their powers are within certain ranges, the covariant higher derivatives cure the superficial divergence of all but a set of one-loop graphs. The finiteness of these latter graphs is ensured by properties of the supergroup and gauge invariance. In the limit Lambda tends to infinity, all the regulator fields decouple and unitarity is recovered in the renormalized pure SU(N) Yang-Mills theory. By demonstrating these properties, we prove that the regularisation works to all orders in perturbation theory.
ISSN:2331-8422
DOI:10.48550/arxiv.0106258