Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry

TL;DR

It is found that the D(-1)- and D1-brane instanton contributions to the hypermultiplet moduli space of type IIB string compactifications on Calabi-Yau threefolds combine with known perturbative and world sheet instanton corrections into a single modular invariant function that determines the hyper Multiplet low-energy effective action.

Abstract

We find the D(-1) and D1-brane instanton contributions to the hypermultiplet moduli space of type IIB string compactifications on Calabi-Yau threefolds. These combine with known perturbative and worldsheet instanton corrections into a single modular invariant function that determines the hypermultiplet low-energy effective acction.

Figures (1)

• Figure 1: Dualities relating vector and hypermultiplet moduli spaces arising in CY compactifications of type II strings. The moduli spaces for vector and hypermultiplets are denoted by $\mathcal{M}_\text{VM}$ and $\mathcal{M}_\text{HM}$, respectively, with their dimensions below in terms of the Hodge numbers $h^{1,2}$ and $h^{1,1}$ of the CY $X$ or its mirror $\tilde{X}$ with $h^{1,1} (\tilde{X})=h^{1,2}(X)$. The lines below indicate the kind of quantum corrections as well as some of the dualities that relate the various moduli spaces. Mirror symmetry is the statement that $\widetilde{\mathcal{M}}_\text{VM/HM}^B=\mathcal{M}_\text{VM/HM}^A$, while the c-map determines $\mathcal{M}_\text{HM}^{B/A}$ at string tree-level in terms of $\mathcal{M}_\text{VM}^{A/B}$.