On N=1 4d Effective Couplings for F-theory and Heterotic Vacua

TL;DR

This paper demonstrates how superpotential and Kahler potential couplings in N=1 supersymmetric compactifications with branes or bundles can be derived using Hodge theory and mirror symmetry, covering F-theory, type II, and heterotic string scenarios.

Contribution

It introduces a method to compute effective couplings from geometric and mirror symmetry techniques for various string compactifications, including non-perturbative corrections.

Findings

Hodge theory and mirror symmetry can compute superpotential and Kahler potential couplings.

Mirror symmetry of four-folds captures non-perturbative corrections on three-folds.

A physical interpretation for Warner's observation relating matrix factorizations and periods is proposed.

Abstract

We show that certain superpotential and Kahler potential couplings of N=1 supersymmetric compactifications with branes or bundles can be computed from Hodge theory and mirror symmetry. This applies to F-theory on a Calabi-Yau four-fold and three-fold compactifications of type II and heterotic strings with branes. The heterotic case includes a class of bundles on elliptic manifolds constructed by Friedmann, Morgan and Witten. Mirror symmetry of the four-fold computes non-perturbative corrections to mirror symmetry on the three-folds, including D-instanton corrections. We also propose a physical interpretation for the observation by Warner that relates the deformation spaces of certain matrix factorizations and the periods of non-compact 4-folds that are ALE fibrations.