Landau-Ginzburg-Saito theory for descendant Gromov-Witten theory on projective line

TL;DR

This paper establishes a correspondence between descendant Gromov-Witten invariants on the projective line and Landau-Ginzburg-Saito theory, demonstrating their equivalence through correlation functions and recursion relations.

Contribution

It introduces a new framework linking descendant GW theory on the projective line with Landau-Ginzburg-Saito theory, including explicit correlation functions and mirror symmetry mapping.

Findings

Correlation functions satisfy key recursion relations.

Mirror symmetry maps GW descendants to LGS observables.

LGS correlation functions match GW invariants with descendants.

Abstract

We define the correlation functions for the descendants in the Landau-Ginzburg-Saito theory. We show that the correlation functions obey puncture, divisor, dilaton, and topological recursion relations. We formulate the map between the descendant observables in the GW theory on the projective line and the descendant observables in the mirror LGS theory. We prove that the LGS correlation functions of the mirror observables are equal to the GW invariants with descendants.