Exploring a simple sector of the Einstein-Maxwell landscape

Abstract

We explore the four dimensional Einstein-Maxwell landscape as a toy model in which we can formulate a sphere compactification stabilized by an electromagnetic field. Replacing the compactification sphere by J spheres, we obtain a simple sector of the (2J+2)-dimensional Einstein-Maxwell landscape. In this toy model, we analyze some properties which are very difficult to uncover in the string theory landscape, including: complete moduli stabilization, stability conditions, and state counting. We also show how to construct anthropic states in this model. A detailed comparison between the main features of this landscape and the Bousso-Polchinski landscape is given. We finally speculate on the impact of these phenomena in the string theory landscape.