F-theory and Dark Energy

I will present compactifications of F-theory a four dimensional spacetime with spatial slices that have the topology of 3-sphere. These solutions may be used as a starting point for solving some of the known problems of the cosmological constant. The 3-sphere is the target space of an SU(2) WZW model which allows for an exact worldsheet analysis. The compactification space is chosen to be a Spin(7) manifold thus giving "half-supersymmetry" in 4D. I will discuss cosmological solutions that resemble Einstein static Universe. These solutions are actually unstable and can either contract or expand, leading to possibly interesting cosmological scenarios. Finally I will discuss the implications of these scenarios for particle physics.