On the String Interpretation of the $t{\bar t}$-geometry

Abstract

We derive the $t{\bar t}$-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 critical ${\hat c}\!=\!3$ case, to arbitrary non critical topological strings is presented. The interplay between the non trivial cohomology of the $b$-antighost, gravitational descendants and $\bar t$-dependence is discussed. The physical picture emerging from this study is that the $\bar t$ (background) dependence of topological strings with non trivial cohomology for the $b$-antighost, is determined by gravitational descendants.