Adjoint bulk scalars and supersymmetric unification in the presence of extra dimensions

There are several advantages of introducing adjoint superfields at intermediate energies around $M=10^{13}$ GeV. Such as (i) gauge couplings still unify (ii) neutrino masses and mixings are produced (iii) primordial lepton asymmetry can be produced. We point out that if adjoint scalars have bulk excitations along with gauge bosons whereas fermions and the doublet scalar live on boundary then N=2 supersymmetric beta functions $\tilde{b_i}$ vanish. Thus even if extra dimensions open up at an intermediate scale $\mu_0$ and all N=2 Yang-Mills fields as well as N=2 matter fields in the adjoint representation propagate in the bulk, still gauge couplings renormalize beyond $\mu_0$ just like they do in 4-dimensions with adjoint scalars. Consequently unification is achieved in the presence to extra dimensions, mass scales are determined uniquely via Renormalization Group Equations(RGE) and unification scale remains high enough to suppress proton decay. This scenario can be falsified if we get signatures of extra dimensions at low energy.