Unification and the Hierarchy from AdS5

TL;DR

This work assesses gauge-coupling unification in a Randall–Sundrum–type warped extra dimension with bulk gauge bosons. By performing a full 5D calculation in AdS$_5$ and employing a holographically motivated, scale-dependent regulator, the authors show that gauge couplings run logarithmically with energy, with 1-loop beta functions effectively enhanced by a factor $I_0(\Lambda)$ that counts KK modes below the strong coupling scale. Unification is shown to be possible for reasonable choices of the cutoff $\Lambda$ and bulk content, though the unification scale is regulator-dependent and accompanied by threshold corrections. The approach provides a coherent framework to connect high-energy unification ideas with TeV-scale phenomenology in warped geometries, offering a non-SUSY avenue for coupling unification and a basis for further refinements. Key formulas include $g_{5D}^2 = R g_{4D}^2$ with $R = k^{-1}\log(k/T)$ and $\beta(g) = -\frac{g^3}{4\pi^2}\big[\cdots I_0^{\cdot,\cdot}(\Lambda)\big]$.

Abstract

In AdS5, the coupling for bulk gauge bosons runs logarithmically, not as a power law. For this reason, one can preserve perturbative unification of couplings. Depending on the cutoff, this can occur at a high scale. We discuss subtleties in the calculation and present a regularization scheme motivated by the holographic correspondence. We find that generically, as in the standard model, the couplings almost unify. For specific choices of the cutoff and number of scalar multiplets, there is good agreement between the measured couplings and the assumption of high scale unification.

Figures (2)

• Figure 1: $I_0(\Lambda)$ as a function of $\Lambda/k$. From top to bottom: massless vector, massive vector (with bulk mass $M=k$), and Dirichlet vector (that is, a vector boson with odd parity under the orbifold transformation).
• Figure 2: $\alpha^{-1}$ as a function of $\log_{10} (M_{G}/M_Z)$. Unification of couplings for $\Lambda = k$ (solid lines). The standard model is shown for comparison (dashed lines).