Construction of Free Energy of Calabi-Yau manifold embedded in $CP^{n-1}$ via Torus Actions

TL;DR

This paper computes correlation functions of the topological A-model on Calabi-Yau hypersurfaces in projective space using torus actions and derives a path-integral representation of the free energy coupled to gravity.

Contribution

It introduces a novel method using torus actions to calculate correlation functions and free energy of the topological sigma model on Calabi-Yau manifolds.

Findings

Correlation functions computed explicitly for Calabi-Yau hypersurfaces.

Path-integral representation of free energy derived.

Method provides new insights into topological string theory calculations.

Abstract

We calculate correlation functions of topological sigma model (A-model) on Calabi-Yau hypersurfaces in $CP^{N-1}$ using torus action method. We also obtain path-integral represention of free energy of the theory coupled to gravity.