Comments on Unparticles
  We comment on several points concerning unparticles which have been overlooked in the literature. One regards Mack's unitarity constraint lower bounds on CFT operator dimensions,e.g. d\geq 3 for primary, gauge invariant, vector unparticle operators. We correct the results in the literature to account for this, and also for a needed correction in the form of the propagator for vector and tensor unparticles. We show that the unitarity constraints can be directly related to unitarity requirements on scattering amplitudes of particles, e.g. those of the standard model, coupled to the CFT operators. We also stress the existence of explicit standard model contact terms, which are generically induced by the coupling to the CFT (or any other hidden sector), and are subject to LEP bounds. Barring an unknown mechanism to tune away these contact interactions, they can swamp interference effects generated by the CFT. We illustrate these points in the context of a weakly coupled CFT example. A significant amount of the unparticle literature should be reconsidered in light of the observations in this note. 
Benjamin Grinstein, Kenneth Intriligator, and Ira Z. Rothstein