Gauge coupling renormalization in RS1

We compute the 4D low energy effective gauge coupling at one-loop order in the compact Randall-Sundrum scenario with bulk gauge fields and charged matter, within controlled approximations. While such computations are subtle, they can be important for studying phenomenological issues such as grand unification. Ultraviolet divergences are cut-off using Pauli-Villars regularization so as to respect 5D gauge and general coordinate invariance. The structure of these divergences on branes and in the bulk is elucidated by a 5D position-space analysis. The remaining finite contributions are obtained by a careful analysis of the Kaluza-Klein spectrum. We comment on the agreement between our results and expectations based on the AdS/CFT correspondence, in particular logarithmic sensitivity to the 4D Planck scale.