  A three-dimensional effective lattice theory of Polyakov loops is derived
from QCD by expansions in the fundamental character of the gauge action, u, and
the hopping parameter, \kappa, whose action is correct to \kappa^n u^m with
n+m=4. At finite baryon density, the effective theory has a sign problem which
meets all criteria to be simulated by complex Langevin as well as by Monte
Carlo on small volumes. The theory is valid for the thermodynamics of heavy
quarks, where its predictions agree with simulations of full QCD at zero and
imaginary chemical potential. In its region of convergence, it is moreover
amenable to perturbative calculations in the small effective couplings. In this
work we study the challenging cold and dense regime. We find unambiguous
evidence for the nuclear liquid gas transition once the baryon chemical
potential approaches the baryon mass, and calculate the nuclear equation of
state. In particular, we find a negative binding energy per nucleon causing the
condensation, whose absolute value decreases exponentially as mesons get
heavier. For decreasing meson mass, we observe a first order liquid gas
transition with an endpoint at some finite temperature, as well as gap between
the onset of isospin and baryon condensation.
