Polynomial Rings and Topological Strings
18.07.2013 at 16:15
I will discuss the construction of a differential polynomial ring from the special geometry of the moduli space of Calabi-Yau threefolds. The higher genus topological string amplitudes can be expressed in terms of the generators of this ring giving them a global description in the moduli space. They can be furthermore computed recursively up to boundary data from the BCOV anomaly equations. Special choices of the generators coincide with quasi modular forms for geometries with duality groups for which these are known. They provide a generalization thereof in the other cases. The action of an involution exchanging two distinguished expansion points of the quasi modular forms is interpreted as a duality of the topological string amplitudes. This is based on joint work with Emanuel Scheidegger, Shing-Tung Yau and Jie Zhou.