Chiral symmetry breaking and restoration in 2+1 dimensions from holography: Magnetic and inverse magnetic catalysis

We study the chiral symmetry breaking and restoration in $ (2+1) $-dimensional gauge theories from the holographic hard and softwall models. We describe the behavior of the chiral condensate in the presence of an external magnetic field for both models at finite temperature. For the hardwall model we find Magnetic Catalysis (MC) in different set ups. For the softwall model we find Inverse Magnetic Catalysis (IMC) and MC in different situations. We also find for the softwall model a crossover transition from IMC to MC at a pseudo-critical magnetic field. This study also shows spontaneous symmetry breaking for both models. Interestingly, for $B=0$ in the softwall model we found a non-trivial expectation value for the chiral condensate.