Holographic QCD Matter: Chiral Soliton Lattices in Strong Magnetic Field

TL;DR

This paper explores the formation of chiral soliton lattices in holographic QCD under strong magnetic fields, revealing their interpretation as D4-branes and analyzing baryon number and pion decay constant modifications.

Contribution

It demonstrates that the ground state in holographic QCD with magnetic fields is a chiral soliton lattice, linking it to D4-branes and instanton structures, and derives magnetic field effects on pion decay.

Findings

Chiral soliton lattice is the ground state in magnetic fields.

Baryon number is unified as instanton charge density.

Pion decay constant depends on magnetic field, matching lattice QCD results.

Abstract

We investigate the chiral soliton lattice (CSL) in the framework of holographic QCD in magnetic field. Under appropriate boundary conditions for the gauge field and the quark mass deformation, we demonstrate that the ground state in the gravitational dual of QCD is given by the CSL in the background magnetic field and the baryon number density. In the presence of the background magnetic field, we show that the CSL is interpreted as a uniformly distributed D4-branes in the holographic setup, where the chiral soliton is identified with a non-self-dual instanton vortex or a center vortex in the five dimensional bulk gauge theory. While the baryon numbers are given to chiral solitons as well as Skyrmions due to the different terms in the Wess-Zumino-Witten (WZW) term in the chiral perturbation theory, these baryon numbers with different origins are unified in terms of the instanton charge density in five dimensions. With bulk analysis of the WZW term, we find that the pion decay constant becomes dependent on the magnetic field. For the massless pion case, we obtain an analytical form that is in qualitative agreement with lattice QCD results for strong magnetic fields.