Type IIB flux vacua from G-theory I

Abstract

We construct non-perturbatively exact four-dimensional Minkowski vacua of type IIB string theory with non-trivial fluxes. These solutions are found by gluing together, consistently with U-duality, local solutions of type IIB supergravity on $T^4 \times \mathbb{C}$ with the metric, dilaton and flux potentials varying along $\mathbb{C}$ and the flux potentials oriented along $T^4$. We focus on solutions locally related via U-duality to non-compact Ricci-flat geometries. More general solutions and a complete analysis of the supersymmetry equations are presented in the companion paper [1]. We build a precise dictionary between fluxes in the global solutions and the geometry of an auxiliary $K3$ surface fibered over $\mathbb{CP}^1$. In the spirit of F-theory, the flux potentials are expressed in terms of locally holomorphic functions that parametrize the complex structure moduli space of the $K3$ fiber in the auxiliary geometry. The brane content is inferred from the monodromy data around the degeneration points of the fiber.