On the RS2 realization of unparticles

Abstract

To facilitate the study of the unparticle scenario it is very desirable to have a treatable model realizing it in four dimensions. Motivated by the general idea of the AdS/CFT correspondence, we consider a simple construction: the Randall-Sundrum 2 (single brane) 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 m_5^2 >= 0, which, unlike in the scalar case, is unchanged from flat space. This condition results in the unitarity bound d_V >= 3, or, more generally, d_V >= D-1 for a vector unparticle in D-dimensional space. It is instructive to consider the RS 2 propagator in (Euclidean) position space: at large distances it behaves as a pure CFT propagator, while at short distances it turns into the 5d flat space propagator. The latter is softer than the former, thus regulating the would-be divergences of the spectral integral and turning the "contact" terms seen at low energies into finite-range interactions. Upon Fourier transforming to momentum space, one finds that at low momenta the CFT piece is subdominant to the "contact" interactions.