Systematics of coupling flows in AdS backgrounds

Abstract

We give an effective field theory derivation, based on the running of Planck brane gauge correlators, of the large logarithms that arise in the predictions for low energy gauge couplings in compactified ${\mathrm{AdS}}_{5}$ backgrounds, including the one-loop effects of bulk scalars, fermions, and gauge bosons. In contrast with the case of charged scalars coupled to Abelian gauge fields that has been considered previously in the literature, the one-loop corrections are not dominated by a single 4D Kaluza-Klein mode. Nevertheless, in the case of gauge field loops, the amplitudes can be reorganized into a leading logarithmic contribution that is identical to the running in 4D non-Abelian gauge theory, and a term which is not logarithmically enhanced and is analogous to a two-loop effect in 4D. In a warped grand unified theory (GUT) model broken by the Higgs mechanism in the bulk, we show that the matching scale that appears in the large logarithms induced by the non-Abelian gauge fields is ${m}_{\mathrm{XY}}^{2}/k$ where ${m}_{\mathrm{XY}}$ is the bulk mass of the XY bosons and k is the AdS curvature. This is in contrast with the UV scale in the logarithmic contributions of scalars, which is simply the bulk mass m. Our results are summarized in a set of simple rules that can be applied to compute the leading logarithmic predictions for coupling constant relations within a given warped GUT model. We present results for both boundary breaking of the GUT gauge group and bulk breaking through the Higgs mechanism.