Rotating Dirac fermions in a magnetic field in 1+2 and 1+3 dimensions

Abstract

We consider the effects of an external magnetic field on rotating fermions in 1+2 and 1+3 dimensions. The dual effect of a rotation parallel to the magnetic field causes a net increase in the fermionic density by centrifugation, which follows from the sinking of the particle lowest Landau level in the Dirac sea for free Dirac fermions. In 1+d=2n dimensions, this effect is related to the chiral magnetic effect in 2n-2 dimensions. This phenomenon is discussed specifically for both weak and strong interfermion interactions in 1+2 dimensions. For QCD in 1+3 dimensions with Dirac quarks, we show that in the strongly coupled phase with spontaneously broken chiral symmetry, this mechanism reveals itself in the form of an induced pion condensation by centrifugation. We use this observation to show that this effect causes a shift in the chiral condensate at leading order in the pion interaction, and to discuss the possibility for the formation of a novel pion superfluid phase in off-central heavy-ion collisions at collider energies.