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

TL;DR

The work analyzes non-perturbative alpha' corrections and modular properties in four-dimensional N=1 type IIB orientifolds with O3/O7 planes. It demonstrates that certain alpha' corrections survive the large-volume limit and must be completed by D-instanton contributions to maintain duality, with the D-instanton superpotential generically depending on two-form moduli through theta-like Jacobi forms in the dilaton τ. By focusing on an orientifold of the Enriques Calabi–Yau, the authors obtain a controlled effective theory where moduli spaces factor into cosets and worldsheet instanton corrections are absent, enabling a precise link between D-instanton data and topological-string degeneracies via the Borcherds function Φ_B. They propose a D3-instanton superpotential for the Enriques case of the form W_D-inst ∝ ∑_n Θ_n(τ,G) e^{inT_S}/η^{10}(τ), with Θ_n satisfying a Jacobi-form-like differential constraint and transforming appropriately under the residual duality, thereby realizing modular invariance in the non-perturbative sector. The results illuminate how holomorphy, duality, and topological-string counting feed into the non-perturbative structure of realistic 4D theories from string theory and suggest concrete routes to compute the Jacobi-form coefficients in explicit models.

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.