Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model

TL;DR

This paper develops a method to compute topological string amplitudes on local toric del Pezzo surfaces using the remodeling the B-model approach, enabling calculations across the entire moduli space and predicting new invariants.

Contribution

It introduces a functional formula for the Bergman kernel applicable to a broad class of local toric del Pezzo surfaces, facilitating amplitude calculations via topological recursion.

Findings

Derived a functional formula for the Bergman kernel applicable to many local toric del Pezzo surfaces.

Computed A-model amplitudes on K_{F_2} using mirror symmetry.

Predicted open orbifold Gromov-Witten invariants of C^3/Z_4.

Abstract

We study topological strings on local toric del Pezzo surfaces by a method called remodeling the B-model which was recently proposed by Bouchard, Klemm, Marino and Pasquetti. For a large class of local toric del Pezzo surfaces we prove a functional formula of the Bergman kernel which is the basic constituent of the topological string amplitudes by the topological recursion relation of Eynard and Orantin. Because this formula is written as a functional of the period, we can obtain the topological string amplitudes at any point of the moduli space by a simple change of variables of the Picard-Fuchs equations for the period. By this formula and mirror symmetry we compute the A-model amplitudes on K_{F_2}, and predict the open orbifold Gromov-Witten invariants of C^3/Z_4.