Perturbative BRST current algebra anomalies for the free bosonic string

A gauged version of the BRST symmetry for a general class of gauge-fixed actions for the bosonic string is used to study the possible anomalies of the corresponding BRST current algebra. One finds that they are rigidly linked to the trace anomaly of the initial theory. A similar analysis is performed for the BRST current algebra associated with the 'conformal-factorized theory' obtained by introducing Beltrami differentials. One finds that the factorization is maintained in the anomalous current algebra theory; again, all the current-algebra anomalies are rigidly linked to the 'holomorphy' anomaly. None of these current algebras is anomalous in the critical dimension. (orig.)