Mirror Symmetry, N=1 Superpotentials and Tensionless Strings on Calabi-Yau Four-Folds

TL;DR

This paper explores the use of mirror symmetry in Calabi-Yau four-folds to analyze F-theory compactifications, focusing on topological invariants, non-perturbative superpotentials, and tensionless strings, with implications for physical theories and supersymmetry breaking.

Contribution

It provides a detailed classification of divisors affecting superpotentials and links physical singularities to tensionless strings in F-theory compactifications.

Findings

Correlation functions determined by divisor rings and period integrals.

Classification of divisors contributing to non-perturbative superpotentials.

Identification of tensionless strings associated with physical singularities.

Abstract

We study aspects of Calabi-Yau four-folds as compactification manifolds of F-theory, using mirror symmetry of toric hypersurfaces. Correlation functions of the topological field theory are determined directly in terms of a natural ring structure of divisors and the period integrals, and subsequently used to extract invariants of moduli spaces of rational curves subject to certain conditions. We then turn to the discussion of physical properties of the space-time theories, for a number of examples which are dual to $E_8\times E_8$ heterotic N=1 theories. Non-critical strings of various kinds, with low tension for special values of the moduli, lead to interesting physical effects. We give a complete classification of those divisors in toric manifolds that contribute to the non-perturbative four-dimensional superpotential; the physical singularities associated to it are related to the apppearance of tensionless strings. In some cases non-perturbative effects generate an everywhere non-zero quantum tension leading to a combination of a conventional field theory with light strings hiding at a low energy scale related to supersymmetry breaking.