Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant

A four-form gauge flux makes a variable contribution to the cosmological constant. This has often been assumed to take continuous values, but we argue that it has a generalized Dirac quantization condition. For a single flux the steps are much larger than the observational limit, but we show that with multiple fluxes the allowed values can form a sufficiently dense `discretuum'. Multiple fluxes generally arise in M theory compactifications on manifolds with non-trivial three-cycles. In theories with large extra dimensions a few four-forms suffice; otherwise of order 100 are needed. Starting from generic initial conditions, the repeated nucleation of membranes dynamically generates regions with a cosmological constant in the observational range. Entropy and density perturbations can be produced.