On the string interpretation of the tt-geometry Original Research Article

We derive the tt-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 critical ĉ = 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.