Higgs as a Holographic Pseudo-Goldstone Boson

TL;DR

The paper presents a holographic framework in which the Standard Model Higgs is a composite pseudo-Goldstone boson protected by a non-linearly realized global symmetry. By mapping a strongly coupled 4D sector to a weakly coupled 5D AdS dual, it demonstrates a finite, radiatively generated Higgs potential with no quadratic divergences, and shows how a tree-level Higgs quartic can be realized via high-energy SU(3)$_L$-breaking dynamics or through gauge-Higgs unification with $A_5$. The one-loop Higgs mass is found to be finite and suppressed relative to the first resonance scale $\ abla \Lambda_{NP} \sim \pi/L_1$, addressing the little hierarchy problem. The framework predicts TeV-scale resonances and distinct Higgs-sector dynamics, offering a UV-complete route distinct from conventional Little Higgs models and with testable collider implications.

Abstract

The AdS/CFT correspondence allows to relate 4D strongly coupled theories to weakly coupled theories in 5D AdS. We use this correspondence to study a scenario in which the Higgs appears as a composite pseudo-Goldstone boson (PGB) of a strongly coupled theory. We show how a non-linearly realized global symmetry protects the Higgs mass and guarantees the absence of quadratic divergences at any loop order. The gauge and Yukawa interactions for the PGB Higgs are introduced in a simply way in the 5D AdS theory, and their one-loop contributions to the Higgs potential are calculated using perturbation theory. These contributions are finite, giving a squared-mass to the Higgs which is one-loop smaller than the mass of the first Kaluza-Klein state. We also show that if the symmetry breaking is caused by boundary conditions in the extra dimension, the PGB Higgs corresponds to the fifth component of the bulk gauge boson. To make the model fully realistic, a tree-level Higgs quartic coupling must be induced. We present a possible mechanism to generate it and discuss the conditions under which an unwanted large Higgs mass term is avoided.

Figures (6)

• Figure 1: One-loop corrections to the PGB mass in the holographic theory from the gauge field (a) and an elementary fermion (b). If the coupling of the source $\chi$ with the conformal sector is relevant, then the fermion propagator in the diagram (b) must be intended as corrected by an infinite series of CFT insertions.
• Figure 2: Contributions to the Higgs quartic coupling. The CFT dynamics is represented as a thick gray line, while a thin black line represents the propagator of the elementary scalar $\varphi$. A cross $\times$ indicates an SU(3)$_L$ breaking by the CFT.
• Figure 3: Contributions to the Higgs mass. The CFT dynamics is represented as a thick gray line, while a thin black line represents the propagator of the elementary scalar $\varphi$. A cross $\times$ indicates an SU(3)$_L$ breaking by the CFT.
• Figure 4: The holographic theory consists of a CFT interacting with an elementary sector represented here by the gauge fields $A_\mu^a$, $A^{\bar{a}}_\mu$ and a generic field $\varphi$. The Goldstone bosons $\pi^{\bar{a}}$ are eaten by the gauge fields $A_\mu^{\bar{a}}$ to form massive vectors; the remaining $\pi^{\hat{a}}$ are PGBs.
• Figure 5: The pattern of symmetry breaking.