N=4 extended MSSM

We investigate a perturbative N=4 sector coupled to the MSSM and show that it allows for a stable vacuum correctly breaking the electroweak symmetry. The particle spectrum of the MSSM is enriched by several new particles stemming out from the new N=4 sector of the theory and a new lepton doublet required to cancel global and gauge anomalies of the theory. Even if the conformal invariance of the N=4 sector is explicitly broken a nontrivial UV behavior of the coupling constants is possible: by studying the renormalization group equations at two loops we find that the Yukawa couplings of the heavy fermionic states flow to a common fixed point at a scale of a few TeVs. The parameter space of the new theory is reduced imposing naturalness of the couplings and soft supersymmetry breaking masses perturbativity of the model at the EW scale as well as phenomenological constraints. Our preliminary results on the spectrum of the theory suggest that the LHC can rule out a significant portion of the parameter space of this model.