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 enrichened 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.Comment: 22 pages, 2 figure
