Meson supercurrents and the Meissner effect in the Sakai-Sugimoto model

TL;DR

This paper explores how magnetic fields influence meson supercurrents and the Meissner effect in a holographic model of QCD, revealing phase transitions between neutral and charged pion condensates under varying magnetic conditions.

Contribution

It analytically investigates the effects of magnetic fields on chiral symmetry breaking phases in the Sakai-Sugimoto model, highlighting the interplay between meson supercurrents and the Meissner effect.

Findings

Magnetic fields induce meson supercurrents in neutral pion condensates.

Charged pion condensates expel magnetic fields via the Meissner effect.

Critical magnetic field triggers a first-order phase transition removing the charged pion condensate.

Abstract

The Sakai-Sugimoto model provides a holographic description for chiral symmetry breaking. We use this model to investigate chirally broken phases in an external magnetic field at finite isospin and baryon chemical potentials. The equations of motion for the bulk gauge fields are solved analytically and the free energy is computed from the Yang-Mills and Chern-Simons contributions to the D8 brane action. In the case of a neutral pion condensate, a magnetic field is found to induce nonzero gradients of the Goldstone boson fields corresponding to meson supercurrents. A charged pion condensate, on the other hand, expels the magnetic field due to the Meissner effect. Upon comparing the Gibbs free energies of these two phases we find that the rotation of the chiral condensate into a charged pion condensate for finite isospin chemical potentials is partially undone by switching on a magnetic field, and we determine the critical magnetic field which removes the charged pion condensate in a first-order phase transition.