https://doi.org/10.1140/epjs/s11734-026-02333-8
Review
Phase structure and observables at high densities from first principles QCD
1
Institut für Theoretische Physik, Justus-Liebig-Universität Gießen, 35392, Giessen, Germany
2
Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung, Campus Gießen, 35392, Giessen, Germany
3
Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120, Heidelberg, Germany
4
ExtreMe Matter Institute EMMI, GSI, Planckstr. 1, 64291, Darmstadt, Germany
a
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Received:
23
December
2025
Accepted:
20
April
2026
Published online:
2
June
2026
Abstract
We provide a short review of the progress made in the past decade with functional QCD in the description of the phase structure of QCD. We summarise the most important technical aspects of the framework, discuss strategies for truncations and address the problem of systematic error estimates. We detail efforts to gauge the approach systematically with lattice QCD at zero chemical potential, also including the physics of the Columbia plot at non-physical quark masses. Our main focus is, however, the high density regime of QCD. We address the predictive power of the functional approach for the appearance of new phases beyond the chiral crossover regime for chemical potentials 
. The onset of this regime may be signalled by a critical end point of the crossover line but may also involve a moat regime or the emergence of an instability that indicates an inhomogeneous phase. Respective results include estimates for the location of the onset of new phases, and predictions for their experimental signatures.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
