  The phase structure of flavoured N=2 SYM on a three sphere in an external
magnetic field is studied. The pairing effect of the magnetic field competes
with the dissociating effect of the Casimir free energy, leading to an
interesting phase structure of confined and deconfined phases separated by a
critical curve of a first order quantum phase transition. At vanishing magnetic
field the phase transition is of a third order. For sufficiently strong
magnetic field, the only stable phase is the confined phase and magnetic
catalysis of chiral symmetry breaking is realized. The meson spectra of the
theory exhibit Zeeman splitting and level crossing and feature a finite jump at
the phase transition between the confined and deconfined phases. At strong
magnetic field the ground state has a massless mode corresponding to the
Goldstone boson associated with the spontaneously broken U(1) R-symmetry
analogous to the eta' meson in QCD.
