Dirichlet branes, or their dual heterotic fivebranes and Horava-Witten walls – can trap non-abelian gauge interactions in their worldvolumes. This has placed on a firmer basis an old idea, according to which we might be living on a brane embedded in a higher-dimensional world. The idea arises naturally in compactifications of type I theory, which typically involve collections of orientifold planes and D-branes. The ‘brane-world’ scenario admits a fully perturbative string description.

In type I string theory the graviton (a closed-string state) lives in the ten-dimensional bulk, while open-string vector bosons are in general localized on lower-dimensional D-branes. Furthermore while closed strings interact to leading order via the sphere diagram, open strings interact via the disk diagram which is of higher order in the genus expansion. The four-dimensional Planck mass and Yang-Mills couplings therefore take the form

α_{U} ∼ g_{I}/(r˜M_{I})^{6-n}

M^{2}_{Planck} ∼ r^{n}r˜^{6-n}M^{8}_{I}/g^{2}

where r is the typical radius of the n compact dimensions transverse to the brane, f the typical radius of the remaining (6-n) compact longitudinal dimensions, M_{I} the type-I string scale and g_{I} the string coupling constant. By appropriate T-dualities we can again ensure that both r and r˜ are greater than or equal to the fundamental string scale. T- dualities change n and may take us either to Ia or to Ib theory (also called I or I’, respectively).

It follows from these formulae that (a) there is no universal relation between M_{Planck}, α_{U }and M_{I} anymore, and (b) tree-level gauge couplings corresponding to different sets of D-branes have radius-dependent ratios and need not unify at all. Thus type-I string theory is much more flexible (and less predictive) than its heterotic counterpart. The fundamental string scale, M_{I}, in particular is a free parameter, even if one insists that α_{U} be kept fixed and of order one, and that the string theory be weakly coupled. This added flexibility can be used to ‘remove’ the order-of magnitude discrepancy between the apparent unification and string scales of the heterotic theory, to lower M_{I} to an intemediate scale or even all the way down to its experimentally-allowed limit of order the TeV. Keeping for instance g_{I}, α_{U } and r˜M_{I} fixed and of order one, leads to the condition

rn ∼ M^{2}_{Planck}/M^{2+n}_{I}

A TeV string scale would then require from n = 2 millimetric to n = 6 fermi-size dimensions transverse to our brane world. The relative weakness of gravity is in this picture attributed to the large transverse spreading of the gravitational flux.