Holographic evolution of gauge couplings

TL;DR

This work investigates how gauge couplings evolve in a warped Randall-Sundrum setup with bulk gauge bosons, interpreting AdS one-loop corrections in the dual 4d theory as a combination of leading CFT insertions and loops of CFT-coupled states. The authors compute the one-loop scalar contribution to low-energy gauge couplings for various GUT-breaking mechanisms, showing that the holographic dual predicts GUT-invariant leading running with subleading corrections determined by the breaking method, whether via boundary conditions or a bulk scalar vev. They analyze breaking through TeV-brane or Planck-brane boundary conditions and via a bulk Higgs-like vev, extracting the associated threshold terms and differential running, and discuss perturbativity and model-building implications. Overall, the results demonstrate that gauge coupling evolution in RS scenarios can be made predictive and controlled by holographic principles, guiding the construction of warped GUTs with consistent high-energy behavior and experimentally viable thresholds.

Abstract

We study the gauge coupling evolution of a unified theory in the compact Randall-Sundrum model with gauge bosons propagating in the bulk. One-loop corrections in AdS are interpreted in the 4d dual theory as the sum of two contributions: CFT insertions subleading in a 1/N expansion and loops of the additional particles coupled to the CFT. We have calculated the scalar loop correction to the low energy gauge couplings both in scenarios where the GUT symmetry is broken by boundary conditions and with the Higgs mechanism. In each case our results are what expected from the holographic dual theory.

Figures (3)

• Figure 1: The brane-brane correlator in AdS corresponds holographically to the free gauge propagator corrected by the LO contribution in $1/N$ of the CFT (of order $\sim {\cal {O}}[N^2 (\alpha/4\pi)]$ with respect to the tree level). The grey circle represents the $\langle JJ \rangle$ insertion.
• Figure 2: The one-loop (rainbow) scalar correction to the brane-brane correlator in AdS corresponds holographically to three different diagrams: a 4d scalar loop graph (a), the same diagram with the scalar propagator corrected by the CFT (c), and the NLO contribution in $1/N$ of the CFT (b). Diagrams (a), (b) are both ${\cal {O}}(\alpha/4\pi)$ with respect to the tree level; diagram (c) is negligible because the scalar coupling to the CFT is $M_{\text{Pl}}$-suppressed. The grey circle (square) represents the $\langle JJ \rangle$ ($\langle OO \rangle$) insertion. A similar holographic interpretation holds for the seagull diagram.
• Figure 3: Contour $\Gamma$ in the complex plane. The crosses along the real axis correspond to the real positive zeros $x_n$ of the function $f$.