Systematics of Coupling Flows in AdS Backgrounds

TL;DR

The paper develops an effective field theory framework for the running of gauge couplings in compactified AdS$_5$ (RS1), showing that large logarithms in low-energy observables arise from Planck-brane correlators and can be computed analogously to 4D RG running. Despite the presence of many KK modes, the leading logarithmic running for non-Abelian gauge fields is universal and matches the 4D beta function, with additional subleading, scheme-dependent contributions. The work provides concrete results for scalars, fermions, and gauge fields, including how GUT-breaking mechanisms (Planck-brane, orbifold, or bulk Higgs) affect the UV scales that enter the logs, notably $m_{XY}^2/k$ for bulk Higgs breaking and power-law behavior when symmetry-breaking scales exceed the AdS curvature $k$. The findings offer practical rules for computing leading-log predictions of coupling relations in warped GUTs and suggest avenues for intermediate-scale unification within a controlled EFT framework, with potential extensions to other bulk couplings beyond gauge sectors.

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_{XY}^2/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.

Figures (3)

• Figure 1: Fig. 1a, represents the 4D Wilson loop. The blob represents all the CFT corrections to the gauge boson two-point function. These corrections can be calculated using the AdS/CFT correspondence by calculating Witten diagrams. At the order we are working, we need to keep the Witten diagrams shown in Figs. 1b, 1c and 2b. The contribution from Fig. 2b gives the universal logarithm discussed in the text, while 1b and 1c represent the contributions from $\delta\Gamma[A(x)]$ which are possibly non-universal but power suppressed.
• Figure 2: Fig. 2a represents additional leading order corrections to the 4D Wilson loop. 2b, and 2c.are the Witten diagrams which would reproduce the two-point function represented by the filled circles in 2a.
• Figure 3: The figure depicts the decomposition of the original non-local terms in the effective action (the blobs on the LHS) into local terms which define the fictitious coupling $g_F(\mu_0)$ and new non-local effective vertices (the blobs on the RHS). An identical decomposition, not shown, is made for the four-point vertex.