Duality of type-II 7-branes and 8-branes

We present a version of ten-dimensional IIA supergravity containing a 9-form potential for which the field equations are equivalent to those of the standard, massless, IIA theory for vanishing 10-form field strength, F-10, and to those of the 'massive' IIA theory for non-vanishing F-10. We present a multi 8-brane solution of these equations that generalizes the 8-brane of Polchinski and Witten. We show that this solution is T-dual to a new multi 7-brane solution of S-1 compactified IIB supergravity, and that the latter is T-dual to the IIA 6-brane, When combined with the Sl(2; Z) U-duality of the type-IIB superstring, the T-duality between type-II 7-branes and 8-branes implies a quantization of the cosmological constant of type-IIA superstring theory. These results are made possible by the construction of a new massive N = 2 D = 9 supergravity theory, We also discuss the 11-dimensional interpretation of these type-II p-branes