Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-09-15
Phys.Lett. B473 (2000) 233-240
Physics
High Energy Physics
High Energy Physics - Theory
14 pages (LaTeX2e), no figs, v2:Local constraint and references added
Scientific paper
10.1016/S0370-2693(99)01511-7
We derive the analogue of the vanishing of the cosmological constant in 3+1 dimensions, T_0^0 = 0, in terms of an integral over components of the energy-momentum tensor of a 4+1 dimensional universe with parallel three-branes, and an additional constraint local to the branes. The basic ingredients are the existence of a static solution of the Einstein equations, and the compactness of the 5th dimension. The corresponding constraints are applied to a general action of scalar fields with arbitrary potentials in the bulk and on the branes. The equations of motion are solved in a linearized approximation in the 5th dimension, whereupon they require the search for extrema of an ``effective potential'', which depends nonlinearly on the action in the bulk and on the branes. The previous constraints then turn into the vanishing of this ``effective potential'' at the extremum.
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