Towards Integrability of Topological Strings I: Three Froms on Calabi-

Abstract

The precise relation between Kodaira-Spencer path integra l and a particular wave function in seven dimensional quadratic field theory is esta blished. The special properties of three-forms in 6d, as well as Hitchin?s action functional , play an important role. The latter defines a quantum field theory similar to Polyakov?s fo rmulation of 2d gravity; the curious analogy with world-sheet action of bosonic string i s also pointed out.