Branes and the gauge hierarchy

If the fundamental type-I string scale is of the order of few TeV, the prob lem of the gauge hierarchy is that of understanding why some dimensions tra nsverse to our brane-world are so large. The technical aspect of this probl em, as usually formulated, is 'why quantum corrections do not modify drasti cally the masses and other parameters of the Standard Model'. We argue that within type-I perturbation theory, the technical hierarchy problem is solv ed (a) if all massless tadpoles cancel locally over distances of order the string length in the transverse space, or (b) if the massless fields with u ncancelled local tadpoles propagate 'effectively' in d(perpendicular to) gr eater than or equal to 2 large transverse dimensions. These restrictions en sure that loop corrections to the Standard Model parameters decouple from t he four-dimensional Planck scale, except when there are uncancelled tadpole s in d(perpendicular to) = 2 in which cast the dependence on M-p is logarit hmic. This latter case is thus singled out as the only one in which the ori gin of the hierarchy would not be attributed entirely to 'out of this world ' bulk physics. The role of the renormalization group equations in summing the leading large logs is replaced by the classical 2d supergravity equatio ns in the transverse space. (C) 1999 Elsevier Science B.V. All rights reser ved.