2d Gravity Coupled to Topological Minimal Models

We discuss the properties of the large phase space of the genus-0 topological minimal $A_{k + 1}$ model coupled to 2d topological gravity. The minimal action is perturbed by adding all possible gravitational descendants with non-trivial couplings which form the infinite-dimensional large phase space. Some general identities (valid on the large phase space) are derived and the puncture and the dilaton equations are obtained as special cases of these results. Finally we show how the couplings to the gravitational descendants can actually be expressed in terms of the flat coordinates defining the small phase space of the theory. Thus eventually the large phase space becomes determined solely by the LG superpotential characterising the matter sector of the coupled model.