Toward minimal composite Higgs models from regular geometries in bottom-up holography

We study a bottom-up, holographic description of a field theory yielding the spontaneous breaking of an approximate SO(5) global symmetry to its SO(4) subgroup. The weakly coupled, six-dimensional gravity dual has regular geometry. One of the dimensions is compactified on a circle that shrinks smoothly to zero size at a finite value of the holographic direction, hence introducing a physical scale in a way that mimics the effect of confinement in the dual four-dimensional field theory. We study the spectrum of small fluctuations of the bulk fields carrying SO(5) quantum numbers, which can be interpreted as spin-0 and spin-1 bound states in the dual field theory. This work supplements an earlier publication focused only on the SO(5) singlet states. We explore the parameter space of the theory, paying particular attention to composite states that have the right quantum numbers to be identified as pseudo-Nambu-Goldstone bosons (PNGBs). We find that in this model the PNGBs are generally heavy, with masses of the same order as other bound states, indicating the presence of a sizeable amount of explicit symmetry breaking in the field-theory side. Nevertheless, we also find a qualitatively new, unexpected result. When the dimension of the fieldtheory operator inducing SO(5) breaking is close to half the space-time dimensionality, there exists a region of parameter space in which the PNGBs and the lightest scalar are both parametrically light in comparison to all other bound states of the field theory. Although this region is known to yield metastable classical backgrounds, this finding might be relevant to model building in the composite Higgs context.

Automated summary

We study a holographic description in this paper which explains the spontaneous breaking of an approximate SO(5) global symmetry to its SO(4) subgroup in a field theory. By analyzing the spectrum of small fluctuations of the bulk fields, we find some important results, including the heavy mass of pseudo-Nambu-Goldstone bosons(PNGBs) and the existence of a specific region in parameter space when the dimension of the field theory operator causing SO(5) breaking is close to half the space-time dimensionality. These findings are significant for model building in the context of composite Higgs.