On the RS2 realization of unparticles

Abstract

We consider the Randall–Sundrum 2 setup with the Standard Model fields on the brane and a massive vector field in the warped bulk. We show that in this model the known properties of vector unparticles – the nontrivial phase of the CFT propagator, the necessity and dominance of contact interactions, the unitarity constraint on the conformal dimension of the operator, and the tensor structure dictated by conformal symmetry – follow by simple inspection of the brane-to-brane propagator. The phase has a physical interpretation as controlling the rate of escape of unparticles into the extra dimension. Requiring the correct sign for the imaginary part of the longitudinal polarization of the propagator, we obtain the unitarity condition m52⩾0, which, unlike in the scalar case, is unchanged from flat space. This condition results in the unitarity bound dV⩾3, or, more generally, dV⩾D−1 for a vector unparticle in D-dimensional space. It is instructive to consider the RS2 propagator in (Euclidean) position space: at large distances it behaves as a pure CFT propagator, while at short distances it turns into the softer 5d flat space propagator. In contrast, in momentum space, at low momenta the CFT piece is subdominant to the “contact” interactions.