Illusory are the conventional anomalies in the conformal-gauge two-dimensional quantum gravity

The exact solution in terms of Wightman functions is given to the BRS-formulated conformal-gauge two-dimensional quantum gravity coupled with D massless scalar fields. The solution is seen to be free of various anomalies. Its anomalous feature appears only in the B-field equation, The nilpotency violation of BRS charge for D not equal 26, found by Kato and Ogawa, is shown to have been caused by their elimination of B-field. Feynman-diagrammatic method and path-integral formalism axe shown to yield misleading results (e.g., FP-ghost number current anomaly), owing to the fact that these approaches are based on T*-product, which does not generally respect field equations.