Complete the three-dimensional holographic phase diagram

Calculate the full three-dimensional temperature–baryon-chemical-potential–isospin-chemical-potential phase diagram in the Witten–Sakai–Sugimoto model, preferably using the decompactified limit consistently across all temperatures, to reconcile the zero-temperature and nonzero-temperature results.

Background

The review presents separate phase diagrams in the temperature–isospin-chemical-potential, temperature–baryon-chemical-potential, and baryon-chemical-potential–isospin-chemical-potential planes. These calculations use different versions of the Witten–Sakai–Sugimoto model, producing inconsistencies such as mismatched phase-transition curves and the absence of chiral restoration in the zero-temperature plane.

A consistent calculation of the full three-dimensional phase structure would provide a unified description of pion-condensed, baryonic, quark, and quarkyonic phases and would remove the ad hoc rescaling used to combine the currently available results.

References

We then address the three planes shown in Fig. \ref{fig:phases3D} (the three-dimensional phase structure in the space spanned by these planes has not been calculated yet).

— Advances in the holographic description of hot and dense QCD matter  (2608.27023 - Kovensky et al., 27 Aug 2026) in Section 1, subsection “Overview”

The generalization of the $D_{RL}$ configuration with 4 discontinuities has not been done yet.

— Advances in the holographic description of hot and dense QCD matter  (2608.27023 - Kovensky et al., 27 Aug 2026) in Section 7, subsection “Isospin-asymmetric holographic baryons” and Section 10

In cold and dense QCD, spatially anisotropic or inhomogeneous phases are expected, for example through a spatially dependent chiral condensate and/or Cooper pair condensate. A candidate phase is the chiral density wave, brought up in the holographic context in Refs.\ , and one may ask if such a modulation affects baryonic matter in the WSS model .

— Advances in the holographic description of hot and dense QCD matter  (2608.27023 - Kovensky et al., 27 Aug 2026) in Section 10, “Future directions”