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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Paul Mansfield

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

Author(s) from Durham

Abstract

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.