Towards Integrability of Topological Strings I: Three-forms on Calabi-Yau manifolds

TL;DR

This paper explores the connection between topological string theory and seven-dimensional quadratic field theory, emphasizing the role of three-forms on Calabi-Yau manifolds and Hitchin's functional in establishing integrability.

Contribution

It establishes a precise relation between the Kodaira-Spencer path integral and a wave function in 7D quadratic field theory, highlighting the significance of three-forms and Hitchin's action.

Findings

Relation between Kodaira-Spencer integral and 7D wave function

Role of three-forms in 6D and Hitchin's functional

Analogy between Hitchin's action and string world-sheet action

Abstract

The precise relation between Kodaira-Spencer path integral and a particular wave function in seven dimensional quadratic field theory is established. 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 formulation of 2d gravity; the curious analogy with world-sheet action of bosonic string is also pointed out.