  In the context of gauge/gravity duality, we study both probe D7-- and probe
D5--branes in global Anti-de Sitter space. The dual field theory is N=4 theory
on R x S^3 with added flavour. The branes undergo a geometrical phase
transition in this geometry as function of the bare quark mass m_q in units of
1/R with R the S^3 radius. The meson spectra are obtained from fluctuations of
the brane probes. First, we study them numerically for finite quark mass
through the phase transition. Moreover, at zero quark mass we calculate the
meson spectra analytically both in supergravity and in free field theory on R x
S^3 and find that the results match: For the chiral primaries, the lowest level
is given by the zero point energy or by the scaling dimension of the operator
corresponding to the fluctuations, respectively. The higher levels are
equidistant. Similar results apply to the descendents. Our results confirm the
physical interpretation that the mesons cannot pair-produce any further when
their zero-point energy exceeds their binding energy.
