Constraints For Topological Strings In $D\geq 1$

TL;DR

This paper derives new correlation function relations in topological string theory, leading to constraints on partition functions, especially for the $ ext{CP}^1$ model, connecting to matrix model dilatation constraints.

Contribution

It introduces novel relations for correlation functions in topological strings and establishes their implications for partition function constraints, linking to matrix models.

Findings

New correlation function relations for each second cohomology class.

Constraints on the sum over genera and degrees of partition functions.

Equivalence with dilatation constraints in the $ ext{CP}^1$ model.

Abstract

New relations of correlation functions are found in topological string theory; one for each second cohomology class of the target space. They are close cousins of the Deligne-Dijkgraaf-Witten's puncture and dilaton equations. When combined with the dilaton equation and the ghost number conservation, the equation for the first chern class of the target space gives a constraint on the topological sum (over genera and (multi-)degrees) of partition functions. For the $\CP^1$ model, it coincides with the dilatation constraint which is derivable in the matrix model recently introduced by Eguchi and Yang.