  We review numerical results for models with gauge group Sp(2N), discussing
the glueball spectrum in the large-N limit, the quenched meson spectrum of
Sp(4) with Dirac fermions in the fundamental and in the antisymmetric
representation and the Sp(4) gauge model with two dynamical Dirac flavours. We
also present preliminary results for the meson spectrum in the Sp(4) gauge
theory with two fundamental and three antisymmetric Dirac flavours. The main
motivation of our programme is to test whether this latter model is viable as a
realisation of Higgs compositeness via the pseudo Nambu Goldstone mechanism and
at the same time can provide partial top compositeness. In this respect, we
report and briefly discuss preliminary results for the mass of the composite
baryon made with two fundamental and one antisymmetric fermion (chimera
baryon), whose physical properties are highly constrained if partial top
compositeness is at work. Our investigation shows that a fully non-perturbative
study of Higgs compositeness and partial top compositeness in Sp(4) is within
reach with our current lattice methodology.
