An Sl(2,Z) multiplet of nine-dimensional type II supergravity theories

We show that only by performing generalized dimensional reductions all poss ible brane configurations are taken into account and one gets the complete lower-dimensional theory. We apply this idea to the reduction of type IIB s upergravity in an SL(2, R)-covariant way and establish T-duality for the ty pe II superstring effective action in the context of generalized dimensiona l reduction giving the corresponding generalized Buscher's T-duality rules. The full (generalized) dimensional reduction involves all the S-duals of D7 -branes: Q7-branes and a sort of composite 7-branes. The three species cons titute an SL(2, Z) triplet. Their presence induces the appearance of the tr iplet of masses of the 9-dimensional theory. The T-duals, including a "KK-8A-brane", which must have a compact transvers e dimension have to be considered in the type IIA side, Compactification of 11-dimensional KK-9M-branes (a.k.a, M9-branes) on the compact transverse d imension give D8-branes while compactification on a world-volume dimension gives KK-sA-branes. The presence of these KK-monopole-type objects breaks t ranslation invariance and two of them given rise to an SL(2, R)-covariant m assive 11-dimensional supergravity whose reduction gives the massive 9-dime nsional type II theories. (C) 1999 Elsevier Science B.V.