  We study a holographic realisation of a composite Higgs model with an
SO(6)/SO(5) symmetry breaking coset in which the top sector includes
colour-neutral twin-partners that reduce the sensitivity of the Higgs mass to
the cut-off. Key to this neutral-naturalness mechanism is a Z2 symmetry that
leaves the Yukawa couplings to the Higgs boson invariant under an exchange of
the top quark and twin top quark, but the symmetry structure of the model means
that the Z2 symmetry is not present in the gauge boson couplings to the Higgs.
Within the calculable framework of holography we construct and study the Higgs
potential. We examine the relation between the Higgs mass, top-partner spectra,
and the input parameters, finding that the presence of the twin-partners pushes
the masses of the lightest coloured top-partners up to approximately 1500 GeV
while the decay constant remains at approximately 700 GeV. Interestingly, no
additional Z2 breaking terms are required to reproduce the observed masses of
the electroweak gauge bosons, Higgs boson, and top quark.
