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Towards a manifestly gauge invariant and universal calculus for Yang-Mills theory

Towards a manifestly gauge invariant and universal calculus for Yang-Mills theory
Towards a manifestly gauge invariant and universal calculus for Yang-Mills theory
A manifestly gauge invariant exact renormalization group for pure $SU(N)$ Yang-Mills theory is proposed, along with the necessary gauge invariant regularisation which implements the effective cutoff. The latter is naturally incorporated by embedding the theory into a spontaneously broken $SU(N|N)$ super-gauge theory, which guarantees finiteness to all orders in perturbation theory. The effective action, from which one extracts the physics, can be computed 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, \eg the choice of covariantisation and the cutoff profile, and, therefore, guides us to a procedure for streamlined calculations.
0323-0465
621-634
Arnone, S.
5df04071-e71a-49fc-8116-20689b579cba
Gatti, A.
68279ba9-587f-4319-b55b-73c4019b23ad
Morris, T.R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Arnone, S.
5df04071-e71a-49fc-8116-20689b579cba
Gatti, A.
68279ba9-587f-4319-b55b-73c4019b23ad
Morris, T.R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6

Arnone, S., Gatti, A. and Morris, T.R. (2002) Towards a manifestly gauge invariant and universal calculus for Yang-Mills theory. Acta Physica Slovaca, 52, 621-634.

Record type: Article

Abstract

A manifestly gauge invariant exact renormalization group for pure $SU(N)$ Yang-Mills theory is proposed, along with the necessary gauge invariant regularisation which implements the effective cutoff. The latter is naturally incorporated by embedding the theory into a spontaneously broken $SU(N|N)$ super-gauge theory, which guarantees finiteness to all orders in perturbation theory. The effective action, from which one extracts the physics, can be computed 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, \eg the choice of covariantisation and the cutoff profile, and, therefore, guides us to a procedure for streamlined calculations.

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More information

Published date: December 2002

Identifiers

Local EPrints ID: 57001
URI: http://eprints.soton.ac.uk/id/eprint/57001
ISSN: 0323-0465
PURE UUID: dd13efdb-17da-4c68-873e-507651e0f054
ORCID for T.R. Morris: ORCID iD orcid.org/0000-0001-6256-9962

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Date deposited: 13 Aug 2008
Last modified: 07 Oct 2020 02:57

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Contributors

Author: S. Arnone
Author: A. Gatti
Author: T.R. Morris ORCID iD

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