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A three-dimensional effective lattice theory of Polyakov loops is derivedfrom QCD by expansions in the fundamental character of the gauge action, u, andthe hopping parameter, \kappa, whose action is correct to \kappa^n u^m withn+m=4. At finite baryon density, the effective theory has a sign problem whichmeets all criteria to be simulated by complex Langevin as well as by MonteCarlo on small volumes. The theory is valid for the thermodynamics of heavyquarks, where its predictions agree with simulations of full QCD at zero andimaginary chemical potential. In its region of convergence, it is moreoveramenable to perturbative calculations in the small effective couplings. In thiswork we study the challenging cold and dense regime. We find unambiguousevidence for the nuclear liquid gas transition once the baryon chemicalpotential approaches the baryon mass, and calculate the nuclear equation ofstate. In particular, we find a negative binding energy per nucleon causing thecondensation, whose absolute value decreases exponentially as mesons getheavier. For decreasing meson mass, we observe a first order liquid gastransition with an endpoint at some finite temperature, as well as gap betweenthe onset of isospin and baryon condensation.

Heavy dense QCD and nuclear matter from an effective lattice theory