The Proca equation in the Randall-Sundrum II background and unparticles

Recently Grinstein, Intriligator and Rothstein (GIR) found a number of important effects in the context of unparticle physics. They showed that coupling CFT vector operators to Standard Model (SM) currents necessarily leads, in a weakly coupled CFT, to contact interactions between the SM currents. These contact interactions are physically important, since in exclusive scattering of SM initial states to SM final states they are found to dominate over the pure and novel CFT contribution. Such interactions are also necessary to resolve certain divergences that appear in the two-point function at integer scaling dimension. We show that all of these features can be obtained when the SM currents are coupled to a massive vector field living in a five-dimensional warped background of the Randall-Sundrum 2 (RS2) scenario, which by the AdS/CFT duality must exhibit certain properties of the CFT. Within the RS2 model we also examine and contrast in detail the scalar and vector position-space correlators at intermediate and large distances. These issues are also considered in the Lykken-Randall model in which the Standard Model fields are assumed to be confined to a tensionless brane in the AdS background geometry. Our results can be seen as a generalization of those results of GIR that do not follow from symmetries to large N, strongly coupled CFTs.