Asymptotic Freedom and the Spectral Index of String Vacua

Topological Strings I am going to tell you about some work I have been doing with Kirill Saraikin and Cumrun Vafa, the first part of which has appeared in [1] and the second part will appear soon [2]. Since this is the first talk in this workshop about topological strings, I would like to start by introducing topological strings and describing some of their properties. For our purposes we will be interested in studying topological strings on a Calabi-Yau 3-fold X. As in the standard string theory, the topological string deals with maps from a genus g Riemann surface Σg into X. This map must satisfy certain conditions, as being holomorphic, etc. The result is an object called the topological partition function Ztop = exp [∑