N= 4 supergravity lagrangian for type-IIB onT6/Bbb Z2orientifold in presence of fluxes andD3-branes

We derive the Lagrangian and the transformation laws of N=4 gaugedsupergravity coupled to matter multiplets whose sigma-model of the scalars isSU(1,1)/U(1)x SO(6,6+n)/SO(6)xSO(6+n) and which corresponds to the effectiveLagrangian of the Type IIB string compactified on the T^6/Z_2 orientifold withfluxes turned on and in presence of n D3-branes. The gauge group is T^12 x Gwhere G is the gauge group on the brane and T^12 is the gauge group on the bulkcorresponding to the gauged translations of the R-R scalars coming from the R-Rfour--form. The N=4 bulk sector of this theory can be obtained as a truncationof the Scherk-Schwarz spontaneously broken N=8 supergravity. Consequently thefull bulk spectrum satisfies quadratic and quartic mass sum rules, identical tothose encountered in Scherk-Schwarz reduction gauging a flat group. This theorygives rise to a no scale supergravity extended with partial super-Higgsmechanism.Comment: 49 pages, LaTex, 2 figures. Misprints corrected, more comments adde