Moduli spaces of non-geometric type II/heterotic dual pairs

Abstract

We study the moduli spaces of heterotic/type II dual pairs in four dimensions with $$ \mathcal{N} $$ N = 2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector multiplets moduli space receives perturbative corrections in the heterotic description only, and non- perturbative correction in both descriptions. We derive explicitely the perturbative corrections to the heterotic four-dimensional prepotential, using the knowledge of its singularity structure and of the heterotic perturbative duality group. We also derive the exact hypermultiplets moduli space, that receives corrections neither in the string coupling nor in α′.

Heterotic/type II duality and non-geometric compactifications

“…With three vector multiplets and one supergravity multiplet, one expects the constant term to be 4 − n H , with n H the number of hypermultiplets remaining in the orbifold theory. An explicit expansion of B (0,0) 2 in power series yields results that match the analysis of the moduli space that will be given in [18]: one finds for instance respectively 20, 10, 4, 2 and 0 massless hypermultiplets in the p = 2, 3, 5, 7 and 13 theories. 7 For each specific value of Q, it is also possible to extract the index Ω 2 (Q) from the formulae given above.…”

“…Furthermore, a large part, if not all, of the K3 moduli are lifted, see [2] for a detailed analysis of the massless spectra and for one-loop partition functions of the models. The moduli spaces of these theories will be analysed in [18].…”

“…These NS5-brane contributions give non-perturbative modifications to the non-geometric Calabi-Yau construction. The corresponding non-perturbative corrections to the prepotential governing the vector moduli space geometry in the low-energy type IIA effective action will be analyzed in a forthcoming publication [18].…”