The goal of this research line is the study of the phase diagram of QCD (the microscopic theory of the strong interactions). Understanding the properties of QCD at finite temperature and finite density, summarized in its phase diagram, is of importance for the physics of heavy ion collisions, very dense stars and the early universe. Calculations of properties of QCD are often extremely demanding, so in some cases it is useful to consider low energy effective theories of the strong interactions. Many of these simpler models such as sigma models or the NJL model share some of the striking features of QCD, like asymptotic freedom, confinement, chiral symmetry breaking and color superconductivity. Some of these theories allow for topologically nontrivial solutions that are also expected to play an important role in QCD. Their influence on the phase structure of QCD, and consequently on the properties of compact stars, is one of the main objectives of this research line. Another main aim is to investigate the possibility of meta-stable states, in particular, CP violating ones, and their potential relevance for the matter-antimatter asymmetry in the universe.

- Personal fellowship by the Royal Netherlands Academy of Arts and Sciences (KNAW), 2001-2007, "Topological aspects of the phase diagram of QCD"
- A "Universitair Stimuleringsfonds" project of the VU University
Amsterdam

- Demonstration that spontaneous CP violation at θ = π requires a minimum instanton interaction strength and that it is an inherently low energy phenomenon. It causes the condition of Son-Stephanov for charged pion condensation at finite isospin chemical potential to be modified.
- First study of the effects of quantum instantons on the
thermodynamics of the CP
^{N}model. Without them an unphysical pressure arises. - Phase diagrams of the three-flavor NJL model, an effective model for low energy QCD, were obtained. Color superconductivity and pion/kaon condensation phases arise and we studied their competition.
- Results on the thermodynamics of O(N) sigma models in 3+1 dimensions show that an often used treatment of UV divergences at finite temperature is not justifiable.
- A full understanding of the pressure (as function of the temperature) of the O(N) nonlinear sigma model in 1+1 dimensions at next-to-leading order in the large N expansion. This is the first study to deal with IR renormalons at finite temperature.

- Ph.D. thesis of Jorn K. Boomsma (2010), "Effects of instanton interactions on the phases of quark matter"
- Article with Jorn K. Boomsma, “The influence of strong magnetic fields and instantons on the phase structure of the two-flavor NJL model”, published in Physical Review D 81 (2010) 074005.
- Article with Jorn K. Boomsma, “The high temperature CP-restoring phase transition at θ = π”, published in Physical Review D 80 (2009) 034019.
- Article by Daniël Boer, Jorn K. Boomsma, “Spontaneous CP violation in the strong interaction at θ = π”, published in Physical Review D 78 (2008) 054027.
- M.Sc. thesis of Sjoerd Hardeman (2007), "Quark matter influence
on the observational properties of compact stars"

- Article by Harmen J. Warringa, “The phase diagram of neutral quark matter with pseudoscalar condensates in the color-flavor locked phase”, e-Print: hep-ph/0606063
- B.Sc. project report of Malou Maris (2006), "Strange quark stars"
- Ph.D. thesis of Harmen J. Warringa (2006), "Thermodynamics of QCD-inspired theories"
- Article by Jens O. Andersen, Daniël Boer, Harmen J. Warringa, “The effects of quantum instantons on the thermodynamics of the CP(N-1) model”, published in Physical Review D 74 (2006) 045028 (7 pp.)
- Article by Harmen J. Warringa, Daniël Boer, Jens O. Andersen, “Color superconductivity vs. pseudoscalar condensation in a three-flavor NJL model”, published in Physical Review D 72 (2005) 014015 (8 pp.)
- Article by Jens O. Andersen, Daniël Boer, Harmen J. Warringa, “Thermodynamics of O(N) sigma models: 1/N corrections”, published in Physical Review D 70 (2004) 116007 (11 pp.)
- Article by Jens O. Andersen, Daniël Boer, Harmen J. Warringa, “Thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions”, published in Physical Review D 69 (2004) 076006 (8 pp.)
- M.Sc. thesis of Paul Becherer (2003), "Chiral symmetry restoration in linear sigma models at finite temperature"