Non-Perturbative Corrections and Modularity in N=1 Type IIB Compactifications

TL;DR

This paper explores non-perturbative corrections and modular properties in type IIB Calabi-Yau orientifolds, revealing how D-instantons and alpha' corrections influence the Kahler potential and superpotential, with implications for effective theories.

Contribution

It demonstrates the survival of certain alpha' corrections at large volume and their modular dependence, providing a detailed analysis of D-instanton effects in orientifold compactifications.

Findings

Non-perturbative alpha' corrections correct the Kahler potential periodically.

D-instanton superpotential depends on two-form moduli and the dilaton.

The Enriques Calabi-Yau example illustrates controlled N=1 effective theory and modular form relations.

Abstract

Non-perturbative corrections and modular properties of four-dimensional type IIB Calabi-Yau orientifolds are discussed. It is shown that certain non-perturbative alpha' corrections survive in the large volume limit of the orientifold and periodically correct the Kahler potential. These corrections depend on the NS-NS two form and have to be completed by D-instanton contributions to transform covariantely under symmetries of the type IIB orientifold background. It is shown that generically also the D-instanton superpotential depends on the two-form moduli as well as on the complex dilaton. These contributions can arise through theta-functions with the dilaton as modular parameter. An orientifold of the Enriques Calabi-Yau allows to illustrate these general considerations. It is shown that this compactification leads to a controlled four-dimensional N=1 effective theory due to the absence of various quantum corrections. Making contact to the underlying topological string theory the D-instanton superpotential is proposed to be related to a specific modular form counting D3, D1, D(-1) degeneracies on the Enriques Calabi-Yau.