Abstract
It is known that a constant magnetic field is a strong catalyst of dynamical chiral symmetry breaking in 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 ()-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 . 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. The same scheme can be applied to the study of the next-to-leading order correction in . We show that the sigma mode is always a lightly bound state with its mass being twice the dynamical fermion mass for arbitrary strength of the magnetic field. Since the dynamics of the collective modes is always dimensional, the finite temperature transition should be of the Kosterlitz-Thouless (KT) type. We determine the KT transition temperature as well as the mass melting temperature as a function of the magnetic field. It is found that the pseudogap domain is enlarged with increasing strength of the magnetic field. The influence of a chiral imbalance or axial chemical potential is also studied. We find that even a constant axial chemical potential can lead to inverse magnetic catalysis of the KT transition temperature in dimensions. The inverse magnetic catalysis behavior is actually the de Haas–van Alphen oscillation induced by the interplay between the magnetic field and the Fermi surface.
- Received 11 July 2014
DOI:https://doi.org/10.1103/PhysRevD.90.056005
© 2014 American Physical Society