The Wave Function Behavior of the Open Topological String Partition Function on the Conifold

TL;DR

This paper computes the all-genus topological string partition function on the conifold with branes, revealing it as a wave function in different polarizations and exploring the implications for Chern-Simons theory and fermionic representations.

Contribution

It introduces a wave function perspective for topological string partition functions on the conifold, connecting brane backgrounds, polarizations, and fermionic operators.

Findings

Partition functions for different brane backgrounds are interpreted as the same wave function in different polarizations.

A free fermion framework extends to geometries beyond C^3, such as the conifold.

Non-perturbative modifications of Chern-Simons theory are necessary for an accurate target space description.

Abstract

We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli space) can be interpreted as the same wave function in different polarizations. This behavior has a natural interpretation in the Chern-Simons target space description of the topological theory. Our detailed analysis however indicates that non-perturbatively, a modification of real Chern-Simons theory is required to capture the correct target space theory of the topological string. We perform our calculations in the framework of a free fermion representation of the open topological string, demonstrating that this framework extends beyond the simple C^3 geometry. The notion of a fermionic brane creation operator arises in this setting, and we study to what extent the wave function properties of the partition function can be extended to this operator.