Compactification for a Three-Brane Universe

A fully realistic and systematic effective field theory model of a 3-brane universe is constructed. It consists of a six-dimensional gravitating spacetime, containing several, approximately parallel (3+1)-dimensional defects, or ``3-branes''. The Standard Model particles are confined to live on one of the 3-branes while different four-dimensional field theories may inhabit the others, in literally a case of ``parallel universes''. The effective field theory is valid up to the six-dimensional Planck scale, where it must be replaced by a more fundamental theory of gravity and 3-brane structure. Each 3-brane induces a conical geometry in the two dimensions transverse to it. Collectively, the curvature induced by the 3-branes can compactify the extra dimensions into a space of spherical topology. It is possible to take the six-dimensional Planck scale to be not much larger than the weak scale, and the compact space not much smaller than a millimeter, thereby realizing the recent proposal by Arkani-Hamed, Dimopoulos and Dvali for eliminating the Gauge Hierearchy Problem. In this case, an extra force is required to stabilize the compact space against collapse. This is provided by a six-dimensional (compact) U(1) gauge field with a magnetic flux quantum trapped in the compact space. The nature of the Cosmological Constant Problem in this scenario is discussed.