Duality symmetric massive type II theories in D = 8 and D = 6 ∗

We study T 2 compactification of massive type IIA supergravity in presence of possible Ramond-Ramond (RR) background fluxes. The resulting theory in D = 8 is shown to possess full SL(2, R) × SL(2, R) T-duality symmetry similar to the massless case. It is shown that elements of duality symmetry interpolate between massive type IIA compactified on T 2 and ordinary type IIA compactified on T 2 with RR 2-form flux. We also discuss relationship between M-theory vacua and massive type IIA vacua. The D8-brane is found to correspond to M-theory ‘pure gravity’ solution which is a direct product of 7-dimensional Minkowski space and a 4-dimensional instanton. We also construct D6-D8 bound state which preserves 1/2 supersymmetries. We then discuss massive IIA compactification on T 4 and point out that when all possible RR fluxes on T 4 are turned on the six-dimensional theory appears to assume a nice SO(4, 4) invariant form.