Magnetic properties of dense holographic QCD

TL;DR

This work addresses how external magnetic fields affect dense, one‑flavor holographic QCD in the Sakai–Sugimoto model. Using the DBI plus Chern–Simons action on the 8‑brane, the authors show that a background magnetic field induces a baryon‑charged gradient of the pseudo‑scalar η′ in the confined phase, and induces a topological axial current in the deconfined phase, with a phase structure that includes a transition to a mixed baryon/pion‑gradient state. The magnetization is paramagnetic in all phases, with nonlinear DBI effects, and the axial current result matches field‑theory expectations in the appropriate limit. Overall, the paper highlights how holographic CS terms encode topological and transport phenomena in dense QCD‑like matter, offering insights into magnetized baryonic matter and its nonlinear magnetic responses.

Abstract

We investigate the Sakai-Sugimoto model at nonzero baryon chemical potential in a background magnetic field both in the confined phase and in the deconfined phase with restored chiral symmetry. In this case the 8-brane Chern-Simons term becomes important. In the confined phase it generates a gradient of the pseudo-scalar "pion", which carries a non-vanishing baryon charge. Above a critical value of the chemical potential there is a second order phase transition to a mixed phase which includes also ordinary baryonic matter. However, at fixed baryon charge density the matter is purely "pion"-gradient above a critical magnetic field. In the deconfined chiral-symmetric phase at nonzero chemical potential the magnetic field induces an axial current. We also compute the magnetization of the baryonic matter and find that it is paramagnetic in all three phases but with nonlinear behavior at large magnetic field.

Figures (8)

• Figure 1: The baryon number density $d$ and the pseudo-scalar gradient $\nabla\varphi$ as functions of $\mu$ for fixed $h = 1$, and as functions of the magnetic field $h$ for fixed $\mu = 0.2$, all with $u_{KK} = 1$.
• Figure 2: Phase diagram in the (a) canonical and (b) grand canonical ensemble.
• Figure 3: The total baryon charge density $d$ and the baryon fraction $n_4 N_c/d$, as functions of $\mu$ for fixed $h=1$ and $u_{KK} = 1$, and as functions of $h$ for fixed $\mu = 3m_4/N_c$ and $u_{KK}=1$.
• Figure 4: The magnetization $M$ (in units of ${\cal N}$) as a function of $h$ in (a) the pseudo-scalar gradient phase for fixed $\mu = 0.2$ and (b) the mixed phase for fixed $\mu = 3m_4/N_c$ (red) and fixed $d =1$ (dashed blue), all with $u_{KK}=1$.
• Figure 5: The magnetic susceptibility $\Delta\chi$ (divided by ${\cal N}$) of the mixed phase as a function of $d$ and $\mu$ for $u_{KK}=1$.