N = 4 supergravity lagrangian for type-IIB on T6/Z 2 orientifold 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) ⊗ SO (6,6 + n)/SO(6) ⊗ SO(6 + n) and which corresponds to the effective lagrangian of the type-IIB string compactifled on the T⁶/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.