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 held 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 weal; 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. [S0556-2821(99)00408-7].