No-scale N=4 supergravity coupled to Yang-Mills: the scalar potential and super Higgs effect

We derive the scalar potential of the effective theory of type IIB orientifold with 3-form fluxes turned on in presence of non abelian brane coordinates. N=4 supergravity predicts a positive definite potential with vanishing cosmological constant in the vacuum of commuting coordinates, with a classical moduli space given by three radial moduli and three RR scalars which complete a (SU(1,1)/U(1))^3 coset, together with the moduli in the Cartan subalgebra U(1)^{rank G} of the gauge group G. Implications for the super Higgs mechanism are also discussed.