SUPERSYMMETRY, P-BRANE DUALITY, AND HIDDEN SPACETIME DIMENSIONS

A global superalgebra with 32 supercharges and all possible central ex tensions is studied in order to extract some general properties of dua lity and hidden dimensions ina theory that treats p-branes democratica lly. The maximal number of dimensions is 12, with signature (10,2), co ntaining one space and one time dimension that are hidden from the poi nt of view of perturbative ten-dimensional string theory or its compac tifications. When the theory is compactified on R(d-1,1) x T-c+1,T-1 w ith d + c + 2 = 12, there are isometry groups that relate to the hidde n dimensions as well as to duality. Their combined intersecting classi fication schemes provide some properties of nonperturbative states and their couplings.