On the String Interpretation of the T ¯ T-geometry

We derive the t ¯ t-equations for generic N = 2 topological field theories as consistency conditions for the contact term algebra of topological strings. A generalization of the holomorphic anomaly equation, known for the criticaî c = 3 case, to arbitrary non critical topological strings is presented. The interplay between the non-trivial cohomology of the b-antighost, gravitational descendants and ¯ t-dependence is discussed. The physical picture emerging from this study is that the ¯ t (background) dependence of topological strings with non-trivial cohomology for the b-antighost, is determined by gravitational descendants.