  We give an explicit example of a composite Higgs model with a
pseudo-Nambu-Goldstone Higgs in which the top Yukawa coupling is generated via
the partial compositeness mechanism. This mechanism requires composite top
partners which are relatively light compared to the typical mass scale of the
strongly coupled theory. While most studies of the phenomenology of such models
have focused on a bottom-up approach with a minimal effective theory, a
top-down approach suggests that that the theory should contain a limit in which
an unbroken global chiral symmetry protects the mass of the top partners, and
the spectrum of the partners satisfies `t Hooft matching conditions. We
therefore consider a model for the UV gauge group which could provide a
solution to the matching conditions, and note that the relatively light
fermions and pseudo-Goldstone bosons fall into complete multiplets of a large
approximate global symmetry. This implies that the spectrum of particles
lighter than a few TeV is non-minimal. Our example illustrates likely features
of a composite Higgs theory, and also serves as an example of a non-chiral
theory with no sign problem and a possible solution to `t Hooft matching
conditions. It would therefore be very interesting for a lattice exploration.
We find in this example that for some low-energy parameters in the effective
theory the top partners can decay into high multiplicity final states, which
could be difficult for the Large Hadron Collider (LHC) to constrain. This may
potentially allow for the top partners to be lighter than those in more minimal
models.
