Tasi 2009 lectures: The Higgs as a Composite Nambu-Goldstone Boson

TL;DR

The paper surveys composite Higgs frameworks in which the Higgs is a pseudo-Nambu-Goldstone boson arising from a new strong sector, addressing the hierarchy problem without fundamental scalars.It develops a symmetry-based formalism (e.g. ${ m SO}(5)/{ m SO}(4)$) to compute the Higgs potential from gauge and fermion loops via form factors and vacuum misalignment parameter $\xi$, and it connects 4D strong dynamics to a 5D holographic description for calculability.By drawing analogies with QCD (pion potential, Weinberg sum rules) and analyzing EW precision ($S$, $T$) and flavor constraints, it shows how a light composite Higgs can be made compatible with data, while predicting deviations in Higgs couplings and a spectrum of resonances that could be tested at colliders.The holographic Higgs realization demonstrates a calculable, finite potential and a concrete bridge between 5D gauge dynamics and 4D composite frameworks, offering a flexible toolkit for model-building and phenomenology.

Abstract

This is an introduction to theories where the Higgs is a composite Nambu-Goldstone boson of a new strongly-interacting dynamics not much above the weak scale. A general discussion is presented based on the pattern of global symmetries at low energy, and the analogy with the QCD pion is analyzed. The last part of the lectures shows how a composite Higgs can emerge as the hologram of a 5-dimensional gauge field.

Figures (16)

• Figure 1: Unitary circle: at energies below (above) the inelastic threshold the amplitude $a_l$ is constrained to lie on (inside) the circle.
• Figure 2: Cartoon of QCD with part of its chiral symmetry gauged by the weak interactions.
• Figure 3: Cartoon of a new Technicolor sector and QCD with part of their global symmetries gauged by the weak interactions.
• Figure 4: Flow to an IR non-perturbative fixed point.
• Figure 5: Cartoon of a strongly interacting EWSB sector with global symmetry ${\cal G}$ broken down to ${\cal H}_1$ at low energy. The subgroup ${\cal H}_0 \subset {\cal G}$ is gauged by external vector bosons.