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The Consistency of Topological Expansions in Field Theory: `BRST Anomalies' in Strings and Yang-Mills

Paul Mansfield
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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 cut-off 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 counter-term in the former case, and by compactification on $S\sp 4$ in the latter.

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Paul Mansfield. 1993-09-04. The Consistency of Topological Expansions in Field Theory: `BRST Anomalies' in Strings and Yang-Mills. https://doi.org/10.1016/0550-3213(94)90583-5

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