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The phase structure of flavoured N=2 SYM on a three sphere in an externalmagnetic field is studied. The pairing effect of the magnetic field competeswith the dissociating effect of the Casimir free energy, leading to aninteresting phase structure of confined and deconfined phases separated by acritical curve of a first order quantum phase transition. At vanishing magneticfield the phase transition is of a third order. For sufficiently strongmagnetic field, the only stable phase is the confined phase and magneticcatalysis of chiral symmetry breaking is realized. The meson spectra of thetheory exhibit Zeeman splitting and level crossing and feature a finite jump atthe phase transition between the confined and deconfined phases. At strongmagnetic field the ground state has a massless mode corresponding to theGoldstone boson associated with the spontaneously broken U(1) R-symmetryanalogous to the eta' meson in QCD.

Flavoured Large N Gauge Theory on a Compact Space with an External Magnetic Field