Alternative proof of Zamolodchikov’sctheorem in dimensionally regularizedσmodels: An operator-product-expansion analysis

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Abstract
Following an operator-product-expansion analysis we show the validity of Zamolodchikov’s c theorem in dimensionally regularized σ models, in full agreement with results of previous analyses in length-cutoff theories. The necessity of introducing ‘‘running coupling constants’’ along renormalization-group trajectories (as advocated by Polyakov in related studies) is emphasized. The global character (with respect to the target space-time manifold) of the analogue of Zamolodchikov’s c function is stressed. Connection with string effective actions is discussed, by showing that an off-shell extension of the central charge coefficient, which generates the on-shell (tree-level) string scattering amplitudes, is sufficient to ensure an off-shell extension of Zamolodchikov’s c function.