N=4 SUPERGRAVITY LAGRANGIAN FOR TYPE IIB ON T**6 / Z(2) IN PRESENCE OF FLUXES AND D3-BRANES

We derive the lagrangian and the transformation laws of N = 4 gauged supergravity coupled to matter multiplets whose σ-model of the scalars is SU(1,1)/U(1)xSO(6,6+n)/SO(6)xSO(6+n) and which corresponds to the effective lagrangian of the type-IIB string compactified on the T6/Bbb Z2 orientifold with fluxes turned on and in presence of n D3-branes. The gauge group is T12⊗G where G is the gauge group on the brane and T12 is the gauge group on the bulk corresponding to the gauged translations of the R-R scalars coming from the R-R four-form. The N = 4 bulk sector of this theory can be obtained as a truncation of the Scherk-Schwarz spontaneously broken N = 8 supergravity. Consequently the full bulk spectrum satisfies quadratic and quartic mass sum rules, identical to those encountered in Scherk-Schwarz reduction gauging a flat group. This theory gives rise to a no scale supergravity extended with partial super-Higgs mechanism.