Dynamical symmetry breaking on a cylinder in magnetic field

We study dynamical symmetry breaking on a cylinder in external magnetic field parallel to the axis of cylinder when magnetic field affects the dynamics of fermions only through the Aharonov-Bohm phase. We find that unlike other previously studied cases magnetic field in our case counteracts the generation of dynamical fermion mass which decreases with magnetic field. There exists also a purely kinematical contribution to the fermion gap which grows linearly with magnetic field. Remarkably, we find that the total fermion gap, which includes both the dynamical and kinematical contributions, always increases with magnetic field irrespectively the values of coupling constant and the radius of cylinder. Thus, although the dynamical mass is suppressed, external magnetic field does enhance the total fermion gap in the spectrum.