No abstract

Considering local conformal field theories on a Riemann surface by coupling conformal matter fields with a complex structure parametrized by a Beltrami differential, the local diffeomorphism cohomology modulo d of the Becchi–Rouet–Stora operator is computed directly by means of the spectral sequences method. Then, thanks to both power counting and locality principles of the Feynman algorithm, the local theory is analyzed. On the one hand, in the ghost number one sector, consistent anomalies turn out to be exactly, after elimination of a trace anomaly involving matter fields, the well‐known holomorphically split diffeomorphism anomaly due to the vacuum. On the other hand, in the ghost number zero sector, local observables of the theory, namely, the vertex operators, are generically calculated, as well as all possible classical actions for Lagrangian conformal model

In this paper we prove Bardeen's conjecture that the anomaly of the Adler-Bardeen-Bell-Jackiw-Schwinger type in gauge models are definitely absent if they are cancelled at the first order of the h perturbation expansion. Our analysis develops within the regularization independent B.P.H.Z. renormalization scheme. We discuss the possible appearance of anomalies in an enlarged class of gauge models admitting soft violations of the Slavnov-Taylor identities which prescribe the gauge transformation properties of the Green functions. By a repeated use of the Callan-Symanzik equation we conclude that the lowest non vanishing contributions to the anomalies must necessarily correspond to the first order in the h perturbation expansion, hence if they are cancelled at this order the theory will be definitely anomaly free.

The mechanism of radiative mass generation is discussed by means of a simple model with spontaneously broken symmetry. We show how this phenomenon induces an infrared breakdown of the usual perturbative approach and proceed to identify a set of reπormalization prescriptions allowing the construction of a new perturbation theory in which the Ward identities of the model are maintained. The original pathologies are reflected in the appearance of square roots and logarithms of the expansion parameter h.