Polynomial Rings and Topological Strings

In these projects, we developed a differential polynomial ring structure which is defined using the special geometry of the moduli spaces of Calabi-Yau threefolds. The higher genus topological string amplitudes are expressed as polynomials in the generators of these rings, giving them a global description in the moduli space. At particular loci, the amplitudes yield the generating functions of Gromov-Witten invariants. We showed that these rings are isomorphic to the rings of quasi-modular forms for threefolds with duality groups for which these are known. For the other cases, they provide generalizations thereof.

Further Literature

Lecture Notes