  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. But we also find a
qualitatively new, unexpected result. When the dimension of the field-theory
operator inducing SO(5) breaking is close to half of 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.
