Abstract
The properties of matter at finite baryon densities play an important role for the astrophysics of compact stars as well as for heavy ion collisions or the description of nuclear matter. Because of the sign problem of the quark determinant, lattice QCD cannot be simulated by standard Monte Carlo at finite baryon densities. I review alternative attempts to treat dense QCD with an effective lattice theory derived by analytic strong coupling and hopping expansions, which close to the continuum is valid for heavy quarks only, but shows all qualitative features of nuclear physics emerging from QCD. In particular, the nuclear liquid gas transition and an equation of state for baryons can be calculated directly from QCD. A second effective theory based on strong coupling methods permits studies of the phase diagram in the chiral limit on coarse lattices.
Highlights
The understanding of the different forms of nuclear matter under extreme conditions plays an increasingly important role for nuclear astrophysics, particle physics and heavy ion collisions
The infamous "sign problem" of QCD, i.e. the fact that the fermion determinant becomes complex with real chemical potential for baryon number μB, prohibits direct Monte Carlo simulations of lattice
Approximate methods are able to circumvent this problem only for small quark chemical potentials μ transition has been found in t=hisμcBo/n3t∼
Summary
The understanding of the different forms of nuclear matter under extreme conditions plays an increasingly important role for nuclear astrophysics, particle physics and heavy ion collisions. A lot of progress has been made recently, but no non-analytic phase transition has been reported in this approach so far [2]. These difficulties motivate the development of effective theories whose sign problem is mild enough to simulate the cold and dense region of QCD. In this contribution I summarise two approaches based on analytic strong coupling expansions of lattice QCD, that achieve this goal in two complementary parameter regions, either for QCD with very heavy quarks in the continuum, or for QCD with light quarks on coarse lattices.
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