Branes and the Gauge Hierarchy

Abstract

If the fundamental type-I string scale is of the order of few TeV, the problem of the gauge hierarchy is that of understanding why some dimensions transverse to our brane-world are so large. The technical aspect of this problem, as usually formulated, is `why quantum corrections do not modify drastically the masses and other parameters of the Standard Model'. We argue that within type-I perturbation theory, the technical hierarchy problem is solved (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 uncancelled local tadpoles propagate `effectively' in $d_\perp \ge 2$ large transverse dimensions. These restrictions ensure that loop corrections to the Standard Model parameters decouple from the four-dimensional Planck scale, except when there are uncancelled tadpoles in $d_\perp =2$ in which case the dependence on $M_P$ is logarithmic. This latter case is thus singled out as the only one in which the origin 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 equations in the transverse space.