Collective modes and Kosterlitz-Thouless transition in a magnetic field in the planar Nambu--Jona-Lasino model

Understand

It is known that a constant magnetic field is a strong catalyst of dynamical chiral symmetry breaking in 2+1 dimensions, leading to generating dynamical fermion mass even at weakest attraction.

• In this work we investigate the collective modes associated with the dynamical chiral symmetry breaking in a constant magnetic field in the (2+1)-dimensional Nambu--Jona-Lasinio model with continuous U(1) chiral symmetry.
• We introduce a self-consistent scheme to evaluate the propagators of the collective modes at the leading order in 1/N.
• The contributions from the vacuum and from the magnetic field are separated such that we can employ the well-established regularization scheme for the case of vanishing magnetic field.