Compactification of Type IIB String Theory on Calabi-Yau Threefolds

TL;DR

The paper addresses how the SL(2,ℤ) S-duality of ten-dimensional Type IIB string theory survives or is modified upon compactification on Calabi–Yau threefolds to four dimensions. It derives the 4D effective action in the large volume limit, analyzes the action of SL(2,ℤ) on the resulting moduli and tensor sectors, and constructs an explicit map to Type IIA on the mirror ilde{Y}_3, including the large complex structure limit prepotential and the c-map relations. By incorporating worldsheet instanton corrections via the IIA prepotential, it shows that the SL(2,ℤ) symmetry is broken by strong coupling effects on the worldsheet, though a perturbative substructure may persist and nonperturbative 4D effects could potentially restore it. The work clarifies the fate of duality symmetries under CY compactifications and provides a concrete framework for matching IIB and IIA descriptions at the level of effective actions and moduli spaces. Its findings have implications for understanding nonperturbative dualities in 4D N=2 vacua and for exploring corrections to the moduli space metrics arising from worldsheet instantons.

Abstract

We study compactifications of type IIB supergravity on Calabi-Yau threefolds. The resulting low energy effective Lagrangian is displayed in the large volume limit and its symmetry properties - with specific emphasis on the SL(2,Z) - are discussed. The explicit map to type IIA string theory compactified on a mirror Calabi-Yau is derived. We argue that strong coupling effects on the worldsheet break the SL(2,Z).