constant in the bulk $M_S$, identified with the ‘string scale’, and fixed by the string tension $\alpha'$, is related to Planck’s constant on the brane $M_P$ ($\simeq~1.2\times 10^{19}$ GeV) by $$(M_S)^{2+d} = (4\pi)^{d/2} ~\Gamma(d/2) ~M_P^2 ~(R_c)^{-d}$$

    which means that for $R_c \sim 0.2$ mm, it is possible to have $M_S$ as low as a TeV for $d \geq 2$. (The normalization of reference [@HLZ] has been adopted here). This solves the gauge hierarchy problem simply by bringing down the scale of new physics (i.e. strong gravity in this case) to about a TeV and thereby providing a natural cut-off to the SM, since the string scale $M_S$ now controls graviton-induced processes on the brane.

-   There are a huge number of massive Kaluza-Klein excitations of the (bulk) graviton field on the brane, with masses $m_n = n/R_c$, and these collectively produce gravitational excitations of electroweak strength, which may be observable at current experiments and those planned in the near future[@Kubyshin].

It is only fair to mention that a major drawback of the ADD model is that it creates a new hierarchy between the ‘string scale’ $M_s \sim 1$ TeV and the size of the extra dimensions $R_c^{-1} \sim
1$ $\mu$eV. 