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 AdS 5 backgrounds, including the one-loop effects of bulk scalars, fermions, and gauge bosons. In contrast to 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 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 2 XY /k where m XY is the bulk mass of the XY bosons and k is the AdS curvature. This is in contrast to 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 bulk Higgs and boundary breaking of the GUT gauge group. * Electronic address: walter@thsrv.lbl.gov † Electronic address: ira@cmuhep2.phys.cmu.edu

Towers of gravitational theories

“…However, if the object has a non-vanishing quadrupole moment Q ij then there is a logarithmic divergence that requires a counterterm operator of the form dτQ ij R µiνj v µ v ν , leading to classical renormalization group logarithms in physical observables [7]. For instance, the composite object obtained by integrating out the orbital scale r in the black hole binary has a Q ij = 0, and so one expects, by the power counting of the EFT, terms of the form v 6 log v relative to the leading order quadrupole power loss which are calculable by renormalization group methods [8]. A typical Feynman diagram that contributes to the renormalization group equations at order v 6 is given in Fig.…”

Gravitational quantum corrections in warped supersymmetric brane worlds

“…In the absence of localized kinetic terms, the matter-independent term in the effective Kähler potential is known from refs. [53,54] (see also [55,56,57] )and has the form ∆Ω eff ≃ c w /(4π 2 ) z 2 0 z −4 1 , where c w ≃ 1.165. Applying the shift, we find…”

Warped supersymmetric grand unification

“…An effective field theory approach to gauge coupling evolution in AdS, based on gauge theory correlators whose external points are on the Planck brane, was obtained in Ref. [12]. Different methods of computing radiative corrections to the low-energy zero-mode gauge couplings were adopted in Ref.…”

“…The issue of gauge coupling evolution in the AdS background has also been discussed recently in Refs. [15,16,17], and analyzed using deconstruction in [18]. However, a fully realistic theory of grand unification in AdS has not been constructed.…”