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The consistency of topological expansions in field theory : “BRST anomalies” in strings and Yang-Mills.

Mansfield, P. (1994) 'The consistency of topological expansions in field theory : “BRST anomalies” in strings and Yang-Mills.', Nuclear physics B., 416 (1). pp. 205-226.


Many field theories of physical interest have configuration spaces consisting of disconnected components. Quantum mechanical amplitudes are then expressed as sums over these components. We use the Faddeev-Popov approach to write the terms in this topological expansion as moduli space integrals. A cutoff is needed when these integrals diverge. This introduces a dependence on the choice of parametrisation of configuration space which must be removed if the theory is to make physical sense. For theories that have a local symmetry this also leads to a breakdown in BRST invariance. We discuss in detail the cases of bosonic strings and Yang-Mills theory, showing how this arbitrariness may be removed by the use of a counterterm in the former case, and by compactification on S4 in the latter.

Item Type:Article
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Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Nuclear Physics B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nuclear Physics B, 416, 1, 21 March 1994, 10.1016/0550-3213(94)90583-5.
Date accepted:25 October 1993
Date deposited:No date available
Date of first online publication:March 1994
Date first made open access:No date available

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