Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections

TL;DR

This paper develops methods to compute topological string amplitudes on Calabi-Yau complete intersections, explores their dualities, and provides explicit formulas for higher genus contributions, advancing understanding of string compactifications and dualities.

Contribution

It introduces comprehensive techniques for calculating topological string amplitudes on Calabi-Yau complete intersections and explores their dualities and geometric transitions.

Findings

Complete list of mirror pairs of Calabi-Yau complete intersections.

Closed formulas for all genus contributions in fiber directions.

Verification of S-duality through topological string partition functions.

Abstract

We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau spaces. These symplectic invariants are used to remove redundancies in examples. The construction of the B-model propagators leads to compatibility conditions, which constrain multi-parameter mirror maps. For K3 fibered Calabi-Yau spaces without reducible fibers we find closed formulas for all genus contributions in the fiber direction from the geometry of the fibration. If the heterotic dual to this geometry is known, the higher genus invariants can be identified with the degeneracies of BPS states contributing to gravitational threshold corrections and all genus checks on string duality in the perturbative regime are accomplished. We find, however, that the BPS degeneracies do not uniquely fix the non-perturbative completion of the heterotic string. For these geometries we can write the topological partition function in terms of the Donaldson-Thomas invariants and we perform a non-trivial check of S-duality in topological strings. We further investigate transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2 quotients that lead to a new class of heterotic duals.