Topological σ models and conformal invariances

A modified version of Witten's model which describes the two-dimensional topological gravity coupled to the topological σ model is given. We find there is a modified superconformal symmetry at the classical level. Furthermore, the superconformal anomaly does not appear at the quantum level and the critical dimension is undetermined. In the superconformal gauge, it is clarified that the physical states belong to the cohomology class of the nilpotential operator which is the direct sum of the fermionic charge Q and the usual Becchi-Rouet-Stora-Tyutin charge s