F-theory and Dark Energy

Motivated by its potential use as a starting point for solving various cosmological constant problems, we study F-theory compactified on the warped product RtimexS3xY8 where Y-8 is a Spin(7) manifold, and the S-3 factor is the target space of an SU(2) Wess-Zumino-Witten (WZW) model at level N. Reduction to M-theory exploits the abelian duality of this WZW model to an S3/ZN orbifold. In the large N limit, the untwisted sector is captured by 11D supergravity. The local dynamics of intersecting 7-branes in the Spin(7) geometry is controlled by a Donaldson-Witten twisted gauge theory coupled to defects. At late times, the system is governed by a 1D quantum mechanics system with a ground state annihilated by two real supercharges, which in four dimensions would appear as N=1/2 supersymmetry on a curved background. This leads to a cancellation of zero point energies in the 4D field theory but a split mass spectrum for superpartners of order Delta m4D similar to MIRMUV specified by the IR and UV cutoffs of the model. This is suggestively close to the TeV scale in some scenarios. The classical 4D geometry has an intrinsic instability which can produce either a collapsing or expanding Universe, the latter providing a promising starting point for a number of cosmological scenarios. The resulting 1D quantum mechanics in the time direction also provides an appealing starting point for a more detailed study of quantum cosmology.