Appears in collection : Mikefest : A conference in honor of Michael Douglas’ 60th birthday

Extra spacetime dimensions give rise to KK fields, whose masses should be large and in particular much larger than the cosmological constant. While this can happen naturally in an effective low-energy theory, it is not the case for most known vacuum solutions of ten-or eleven-dimensional supergravity. We review efforts to find vacua that resolve this tension and recent general bounds on KK masses.