On the Genus Expansion in the Topological String Theory

TL;DR

This paper develops a systematic approach to higher genus expansions in topological string theory, introduces methods for genus zero correlation functions, and explores the structure of free energy in specific models, revealing limitations in certain minimal models.

Contribution

It provides a new systematic formulation for higher genus expansions and evaluates genus zero correlation functions, with new results on the $CP^1$ model and insights into minimal models.

Findings

Formulas for free energy in $A_1$ and $A_2$ models.

Evidence that non-A-D-E minimal models lack higher genus expansions beyond genus one.

New results on the $CP^1$ model at higher genera.

Abstract

A systematic formulation of the higher genus expansion in topological string theory is considered. We also develop a simple way of evaluating genus zero correlation functions. At higher genera we derive some interesting formulas for the free energy in the $A_1$ and $A_2$ models. We present some evidence that topological minimal models associated with Lie algebras other than the A-D-E type do not have a consistent higher genus expansion beyond genus one. We also present some new results on the $CP^1$ model at higher genera.