ABSTRACT
Arkani-Hamed, Dimopoulos and Dvali(ADD) recently proposed a interesting low scale quantum gravity scenario which offers a new slant on the hierarchy problem[l]. In its simplest form, gravity is allowed to live in n 'large' extra dimensions, i.e., 'the bulk', while the Standard Model(SM) fields lie on a 3-D surface or brane, 'the wall'. Gravity then becomes strong in the full 4 + n-dimensional space at a scale Ms '" a few Te V which is far below the conventional Planck scale, Mpi '" 1019 GeV. The scales Ms and Mpl are simply related via Gauss' Law:
with Vn being the volume of the compactified extra dimensions. For n extra dimensions of the same size, the simplest possibility, termed a symmetric compactification, Vn '" Rn and one finds that R '" 1030/n-19 meters assuming Ms '" 1 TeV. Note that for separations between two masses less than R the gravitational force law becomes 1/ r2+n. For n = 1, R '" lOll meters and is thus obviously excluded, but, for n = 2 one obtains R '" 0.1 mm, which is at the edge of the sensitivity for existing experiments[2]. One can imagine more general scenarios, termed asymmetric compactifications,
where, e.g., there are p 'small' dimensions that have sizes of", l/TeV with the effective number of 'large' extra dimensions being He!! = n - p, where now n = 6 or 7 as suggested by string theory[3]. Astrophysics [4] requires that Ms > 110 TeV for n = 2 but only 2: a few TeV for n > 2.
