A global superalgebra with 32 supercharges and all possible central extensions is studied in order to extract some general properties of duality and hidden dimensions in a theory that treats $p$-branes democratically. The maximal number of dimensions is 12, with signature (10,2), containing one space and one time dimension that are hidden from the point of view of perturbative ten-dimensional string theory or its compactifications. When the theory is compactified on $R^{d-1,1\mathrm{}}\otimes T^{c+1,1\mathrm{}}$ with $d+c+2=12\mathrm{}$, there are isometry groups that relate to the hidden dimensions as well as to duality. Their combined intersecting classification schemes provide some properties of nonperturbative states and their couplings.

• Received 23 April 1996

DOI:https://doi.org/10.1103/PhysRevD.54.5203