Continuum superpartners from supersymmetric unparticles

We examine supersymmetric theories with approximately conformal sectors. Without an IR cutoff the theory has a continuum of modes, which are often referred to as 'unparticles'. Making use of the AdS/CFT correspondence we find that in the presence of a soft-wall, a gap in the spectrum can arise, separating the zero-modes from the continuum modes. In some cases there are also discrete massive levels in the gap. We also show that when supersymmetry is broken the superpartner of a quark or lepton may simply be a bosonic continuum above a gap. Such extensions of the standard model have novel signatures at the LHC.