Topological Field Theories and the Period Integrals

TL;DR

This paper explores the connection between topological Landau-Ginzburg theories coupled to 2D gravity and period integrals, showing that correlation functions are expressed as these integrals, with examples including A-D-E models.

Contribution

It establishes a precise correspondence between correlation functions in topological Landau-Ginzburg theories and period integrals, revealing a new mathematical structure in these theories.

Findings

Correlation functions match period integrals

Recursion relations align with Gauss-Manin equations

Examples include A-D-E minimal models and $c=3$ theories

Abstract

We discuss topological Landau-Ginzburg theories coupled to the 2-dimensional topological gravity. We point out that the basic recursion relations for correlation functions of the 2-dimesional gravity have exactly the same form as the Gauss-Manin differential equations for the period integrals of superpotentials. Thus the one-point functions on the sphere of the Landau-Ginzburg theories are given exactly by the period integrals. We discuss various examples, A-D-E minimal models and the $c=3$ topological theories.