Supersymmetric large extra dimensions are small and/or numerous

Recently, a scenario has been proposed in which the gravitational scale could be as low as the TeV scale, and extra dimensions could be large and detectable at the electroweak scale. Although supersymmetry is not a requirement of this scenario, it is nevertheless true that its best-motivated realizations arise in supersymmetric theories (such as M theory). We argue here that supersymmetry can have robust, and in some instances fatal, …