Diffeomorphism cohomology in Beltrami parametrization

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 models