I will describe the properties of a quantum field theory in compact space subjected to an external magnetic field. In the context of the AdS/CFT correspondence this is realized by introducing flavour branes to the $AdS_5 \times S^5$ geometry in global coordinates. The dual field theory lives on a round three sphere. The theory has a finite Casimir free energy having dissociating effect on the fundamental condensate of the theory. This competes with the pairing effect of the magnetic field leading to an interesting phase structure.