c=1 String as the Topological Theory of the Conifold

TL;DR

This paper demonstrates that the non-critical c=1 string theory at the self-dual radius is equivalent to topological strings on a deformed conifold, revealing universal behavior of the partition function near conifold points.

Contribution

It establishes a precise equivalence between c=1 string theory at the self-dual radius and topological strings on a conifold, connecting non-critical strings to Calabi-Yau geometry.

Findings

Genus expansion of c=1 string matches topological string partition function

Universal behavior near conifold points identified

Penner sum reproduces the free energy expansion

Abstract

We show that the non-critical $c=1$ string at the self-dual radius is equivalent to topological strings based on the deformation of the conifold singularity of Calabi-Yau threefolds. The Penner sum giving the genus expansion of the free energy of the $c=1$ string theory at the self-dual radius therefore gives the universal behaviour of the topological partition function of a Calabi-Yau threefold near a conifold point.