Inverse magnetic catalysis and the Polyakov loop

TL;DR

This paper explains how an external magnetic field causes inverse magnetic catalysis in QCD by affecting the Polyakov loop and low quark modes, supported by lattice simulations and emphasizing the importance of the Polyakov loop in models.

Contribution

It identifies the sea and valence mechanisms influencing the quark condensate under magnetic fields and highlights the role of the Polyakov loop in inverse magnetic catalysis.

Findings

Sea effect suppresses condensate near transition temperature.

Valence effect enhances condensate under magnetic field.

Lattice simulations confirm the physical mechanism.

Abstract

We study the physical mechanism of how an external magnetic field influences the QCD quark condensate. Two competing mechanisms are identified, both relying on the interaction between the magnetic field and the low quark modes. While the coupling to valence quarks enhances the condensate, the interaction with sea quarks suppresses it in the transition region. The latter `sea effect' acts by ordering the Polyakov loop and, thereby, reduces the number of small Dirac eigenmodes and the condensate. It is most effective around the transition temperature, where the Polyakov loop effective potential is flat and a small correction to it by the magnetic field can have a significant effect. Around the critical temperature, the sea suppression overwhelms the valence enhancement, resulting in a net suppression of the condensate, named inverse magnetic catalysis. We support this physical picture by lattice simulations including continuum extrapolated results on the Polyakov loop as a function of temperature and magnetic field. We argue that taking into account the increase in the Polyakov loop and its interaction with the low-lying modes is essential to obtain the full physical picture, and should be incorporated in effective models for the description of QCD in magnetic fields in the transition region.