Holographic Nuclear Physics

TL;DR

This work analyzes the Sakai–Sugimoto holographic QCD model at finite temperature and baryon chemical potential, focusing on how baryon density is realized via either 4-branes wrapped on $S^4$ (nuclear matter) or strings ending on the 8-branes (quark matter). By solving the D8-brane actions with cusp boundary conditions and comparing the grand potentials, the authors show that the nuclear-matter phase (4-brane cusps) dominates over the quark-matter phase (string cusps) and that the quark-matter configuration is thermodynamically unstable to density fluctuations. In the confined phase, there is a second-order transition from vacuum to nuclear matter at $\mu_{onset}$; in the deconfined phase, a three-region phase diagram emerges with vacuum, nuclear matter, and QGP, including a dip in the nuclear–QGP competition driven by cusp dynamics. The results reproduce qualitative QCD-like features, such as persistent chiral symmetry breaking at high density in the deconfined phase, and provide an equation of state and entropy scaling across phases, offering a holographic handle on finite-density QCD phenomena and guiding future explorations of nonuniform or interacting baryon configurations.

Abstract

We analyze the phases of the Sakai-Sugimoto model at finite temperature and baryon chemical potential. Baryonic matter is represented either by 4-branes in the 8-branes or by strings stretched from the 8-branes to the horizon. We find the explicit configurations and use them to determine the phase diagram and equation of state of the model. The 4-brane configuration (nuclear matter) is always preferred to the string configuration (quark matter), and the latter is also unstable to density fluctuations. In the deconfined phase the phase diagram has three regions corresponding to the vacuum, quark-gluon plasma, and nuclear matter, with a first-order and a second-order phase transition separating the phases. We find that for a large baryon number density, and at low temperatures, the dominant phase has broken chiral symmetry. This is in qualitative agreement with studies of QCD at high density.

Figures (17)

• Figure 1: The phases of holographic QCD at finite temperature and baryon chemical potential. A particular deconfinement temperature (0.025) was chosen for illustration purpose only.
• Figure 2: The 8-brane configuration with $d=0$ and $d\neq 0$ in the confined phase.
• Figure 3: The position of the cusp (and 4-brane) in the 8-brane as a function of the electric displacement $d$ for $l=1$ in the confined phase. We present this as a log plot to show both the initial decrease, as well as the limiting value at large $d$.
• Figure 4: Possible 8-brane configurations with $d=0$ and $d\neq 0$ in the deconfined phase.
• Figure 5: The position of the cusp in the 4-brane cusp configuration as a function of the electric displacement for $l=1$ in the deconfined phase.