Type IIB flux vacua from G-theory I

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 T⁴ × ℂ with the metric, dilaton and flux potentials varying along ℂ and the flux potentials oriented along T⁴. 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 ℂℙ¹. 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.