Topological Field Theory and Rational Curves

TL;DR

This paper explores the relationship between topological field theories and rational curves on Calabi-Yau threefolds, providing a compactification approach that supports a key conjecture in string theory.

Contribution

It introduces a natural compactification of the moduli space of multiple covers of rational curves, aligning with a significant conjecture in the field.

Findings

Derived a formula consistent with the conjecture by Candelas et al.

Analyzed the structure of rational curves in the context of topological sigma-models.

Connected the geometry of Calabi-Yau manifolds with string theory predictions.

Abstract

We analyze the superstring propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear sigma-model and the structure of rational curves on the Calabi-Yau manifold. We study in detail the case of the world-sheet of the string being mapped to a multiple cover of an isolated rational curve and we show that a natural compactification of the moduli space of such a multiple cover leads to a formula in agreement with a conjecture by Candelas, de la Ossa, Green and Parkes.