Topological Strings on Grassmannian Calabi-Yau manifolds

TL;DR

This paper computes higher genus topological string amplitudes on Grassmannian Calabi-Yau manifolds using B-model techniques and mirror symmetry, providing evidence for a conformal field theory description.

Contribution

It introduces a method to solve the B-model for Grassmannian Calabi-Yau manifolds via holomorphic anomaly equations and supports a mirror conjecture with BPS state integrality.

Findings

Explicit higher genus amplitudes computed

Evidence supporting the mirror conjecture

Strong BPS integrality results

Abstract

We present solutions for the higher genus topological string amplitudes on Calabi-Yau-manifolds, which are realized as complete intersections in Grassmannians. We solve the B-model by direct integration of the holomorphic anomaly equations using a finite basis of modular invariant generators, the gap condition at the conifold and other local boundary conditions for the amplitudes. Regularity of the latter at certain points in the moduli space suggests a CFT description. The A-model amplitudes are evaluated using a mirror conjecture for Grassmannian Calabi-Yau by Batyrev, Ciocan-Fontanine, Kim and Van Straten. The integrality of the BPS states gives strong evidence for the conjecture.