THEORIES WITH 2 TIMES

General considerations on the unification of A-type and B-type supersy mmetries in the context of interacting p-branes strongly suggest that the signature of spacetime includes two timelike dimensions. This lead s to the puzzle of how ordinary physics with a single timelike dimensi on emerges. In this letter we suggest that the two timelike dimensions could be real, and belong to two physical sectors of a single theory each containing its own timelike dimension. Effectively there is a sin gle time evolution parameter. We substantiate this idea by constructin g certain actions for interacting p-branes with signature (n, 2) that have gauge symmetries and constraints appropriate for a physical inter pretation with no ghosts. In combination with related ideas and genera l constraints in S-theory, we are led to a cosmological scenario in wh ich, after a phase transition, the extra timelike dimension becomes pa rt of the compactified universe residing inside microscopic matter. Th e internal space, whose geometry is expected to determine the flavor q uantum numbers of low energy matter, thus acquires a Minkowski signatu re. The formalism meshes naturally with a new supersymmetry in the con text of field theory that we suggested in an earlier paper. The struct ure of this supersymmetry gives rise to a new Kaluza-Klein type mechan ism for determining the quantum numbers of low energy families, thus s uggesting that the extra timelike dimension would be taken into accoun t in understanding the standard model of particle physics. (C) 1997 El sevier Science B.V.