Effective Action and Holography in 5D Gauge Theories

TL;DR

The paper develops a holographic framework for 5D gauge theories on warped intervals, explicitly including the scalars from the fifth dimension as a 4D Goldstone matrix $\Sigma$ to form the holographic action. This allows a streamlined computation of the one-loop Higgs potential in Gauge-Higgs Unification and the χPT Lagrangian up to ${\mathcal{O}}(p^4)$ in AdS/QCD, while clarifying how a 5D Chern–Simons term induces a gauged WZW term and the Adler–Bardeen anomaly. The authors provide concrete results for SU(2)$\to$U(1) toy models and derive explicit χPT coefficients (e.g., $L_1$, $L_{10}$) from holography, matching previous KK analyses. Overall, the work offers a unified, more efficient 5D-to-4D effective-field-theory toolkit for both Beyond-Standard-Model Higgs scenarios and QCD-like theories, with clear implications for phenomenology and model-building.

Abstract

We apply the holographic method to 5D gauge theories on the warped interval. Our treatment includes the scalars associated with the fifth gauge field component, which appear as 4D Goldstone bosons in the holographic effective action. Applications are considered to two classes of models in which these scalars play an important role. In the Composite-Higgs (and/or Gauge-Higgs Unification) scenario, the scalars are interpreted as the Higgs field and we use the holographic recipe to compute its one-loop potential. In AdS/QCD models, the scalars are identified with the mesons and we compute holographically the Chiral Perturbation Theory Lagrangian up to p^4 order. We also discuss, using the holographic perspective, the effect of including a Chern-Simons term in the 5D gauge Lagrangian. We show that it makes a Wess-Zumino-Witten term to appear in the holographic effective action. This is immediately applied to AdS/QCD, where a Chern-Simons term is needed in order to mimic the Adler-Bardeen chiral anomaly.