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

Diego M Rodrigues,Danning Li,Henrique Boschi-Filho,Eduardo Folco Capossoli

doi:10.1103/physrevd.98.106007

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.

Highlights

Much theoretical progress on the nonperturbative physics of relativistic quantum field theories (RQFT) has been achieved recently
We present our results for the hardwall model concerning the dependence of the chiral condensate, σ, with the external magnetic field, B, for T 1⁄4 0 and some finite temperatures
Unlike the results for the hardwall model in the previous section, one observes that the chiral condensate in the softwall model presents two different behaviors depending on the value of the magnetic field

Summary

INTRODUCTION

Much theoretical progress on the nonperturbative physics of relativistic quantum field theories (RQFT) has been achieved recently. In the context of lattice QCD, for the chiral phase transition, an inverse magnetic catalysis (IMC) has been observed, i.e., the decreasing of the critical temperature (Tc)with increasing magnetic field (B) for eB ∼ 1 GeV2 [13] and more recently for eB ∼ 3 GeV2 [14]. A promising approach to investigate the phenomena of IMC and MC is based on the AdS=CFT correspondence, or holographic duality [15,16,17,18] Such duality has become very useful to address strongly coupled gauge theories, including the nonperturbative regime of QCD.

Background geometry

Holographic setup for chiral symmetry breaking

Zero temperature case

RESULTS

DISCUSSION AND CONCLUSION