  We elucidate and extend the conditions that map gauge-Yukawa theories at low
energies into time-honoured gauged four-fermion interactions at high energies.
These compositeness conditions permit to investigate theories of composite
dynamics through gauge-Yukawa theories. Here we investigate whether
perturbative gauge-Yukawa theories can have a strongly coupled limit at
high-energy, that can be mapped into a four-fermion theory. Interestingly, we
are able to precisely carve out a region of the perturbative parameter space
supporting such a composite limit. This has interesting implications on our
current view on models of particle physics. As a template model we use an
$SU(N_C)$ gauge theory with $N_F$ Dirac fermions transforming according to the
fundamental representation of the gauge group. The fermions further interact
with a gauge singlet complex $N_F\times N_F$ Higgs that ceases to be a physical
degree of freedom at the ultraviolet composite scale, where it gives away to
the four-fermion interactions. We compute the hierarchy between the ultraviolet
and infrared composite scales of the theory and show that they are naturally
large and well separated. Our results show that some weakly coupled
gauge-Yukawa theories can be viewed, in fact, as composite theories. It is
therefore tantalising to speculate that the standard model, with its
phenomenological perturbative Higgs sector, could hide, in plain sight, a
composite theory.
