Chiral Symmetry Breaking and Restoration in (2+1) Dimensions from Holography: Magnetic and Inverse Magnetic Catalysis

TL;DR

This paper investigates how external magnetic fields influence chiral symmetry breaking and restoration in (2+1)-dimensional gauge theories using holographic models, revealing phenomena like magnetic catalysis, inverse magnetic catalysis, and a crossover transition.

Contribution

It compares hardwall and softwall holographic models to analyze magnetic effects on chiral symmetry, discovering inverse magnetic catalysis and a transition between different magnetic behaviors.

Findings

Hardwall model exhibits magnetic catalysis.

Softwall model shows inverse magnetic catalysis and magnetic catalysis.

A crossover transition occurs at a pseudocritical magnetic field.

Abstract

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 pseudocritical magnetic field. This study also shows spontaneous symmetry breaking for both models. Interestingly, for $B=0$ in the softwall model we found a nontrivial expectation value for the chiral condensate.