Supersymmetry, p-brane duality, and hidden spacetime dimensions.

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 dimensions that are hidden from the point of view of perturbative 10-dimensional string theory or its compactifications. When the theory is compactified on Rd−1,1 ⊗ T c+1,1 with d + c + 2 = 12, there are isometry groups that relate to the hidden dimensions as well as to duality. Their combined intersecting classification schemes provide some properties of non-perturbative states and their couplings. ∗Research supported by DOE grant No. DE-FG03-44ER-40168