A critical cosmological constant from millimeter extra dimensions

We consider 'brane universe' scenarios with standard-model fields localized on a 3-brane in 6 spacetime dimensions. We show that if the spacetime is r otationally symmetric about the brane, local quantities in the bulk are ins ensitive to the couplings on the brane. This potentially allows compactific ations where the effective 4-dimensional cosmological constant is independe nt of the couplings on the 3-brane. We consider several possible singularit y-free compactification mechanisms, and find that they do not maintain this property. We also find solutions with naked spacetime singularities, and w e speculate that new short-distance physics can become important near the s ingularities and allow a compactification with the desired properties. The picture that emerges is that standard-model loop contributions to the effec tive 4-dimensional cosmological constant can be cut off at distances shorte r than the compactification scale. At shorter distance scales, renormalizat ion effects due to standard-model fields renormalize the 3-brane tension, w hich changes a deficit angle in the transverse space without affecting loca l quantities in the bulk. For a compactification scale of order 10(-2) mm, this gives a standard-model contribution to the cosmological constant in th e range favored by cosmology.