  We study Sp(2$N_c$) gauge dynamics with two Dirac fermion flavours in the
fundamental representation. These strongly coupled systems underlie some
composite Higgs models with a global symmetry breaking pattern
SU(4)$\rightarrow$Sp(4), leading to a light quartet of pseudo-Goldstone bosons
that can play the role of the Higgs. Including four-fermion interactions can
rotate the vacuum to a technicolour breaking pattern. Using gauge/gravity
duality, we study the underlying gauge dynamics. Our model incorporates the
$N_c$-specific running of the fermion anomalous dimension and can thus
distinguish between specific gauge groups. We determine the bound-state
spectrum of the UV SU(4)$\rightarrow$Sp(4) symmetry breaking model, also
including fermion masses and mass splitting, and display the $N_c$ dependence.
The inclusion of a four-fermion interaction shows the emergence of three
Goldstone bosons on the path to technicolour dynamics.
