Calculation of Gromov-Witten invariants for $ CP^{3},CP^{4}$,and $Gr(2,4)$

TL;DR

This paper derives recursion relations for Gromov-Witten invariants of $CP^3$, $CP^4$, and $Gr(2,4)$ using topological sigma models, enabling the calculation of rational curves intersecting submanifolds.

Contribution

It introduces a method to compute Gromov-Witten invariants for specific target spaces via associativity relations in topological sigma models, providing new recursive formulas.

Findings

Recursion relations for Gromov-Witten invariants derived

Evaluation of invariants up to certain instanton orders

Number of rational curves intersecting submanifolds calculated

Abstract

Using the associativity relations of the topological Sigma Models with target spaces, $CP^3, CP^4$ and $Gr(2,4)$ , we derive recursion relations of their correlation and evaluate them up to certain order in the expansion over the instantons. The expansion coeffieients are regarded as the number of rational curves in $CP^3, CP^4$ and $Gr(2,4)$ which intersect various types of submanifolds corresponding to the choice of BRST invariant operators in the correlation functions.