Remarks on tree-level topological string theories

TL;DR

This paper discusses topological string theories at the tree level, presenting a variational approach to solutions and extending residue formulas for specific models, enhancing understanding of their mathematical structure.

Contribution

It introduces a variational framework for solving tree-level topological string theories and extends residue formulas to large phase spaces for $A_k$ Landau-Ginzburg models.

Findings

Tree-level solutions expressed via a variational problem.

Extension of residue formulas to large phase space.

Insights into the mathematical structure of topological string theories.

Abstract

A few observations concerning topological string theories at the string-tree level are presented: (1) The tree-level, large phase space solution of an arbitrary model is expressed in terms of a variational problem, with an ``action'' equal, at the solution, to the one-point function of the puncture operator, and found by solving equations of Gauss-Manin type; (2) For $A_k$ Landau-Ginzburg models, an extension to large phase space of the usual residue formula for three-point functions is given.