  The fermion-sign problem at finite density is a persisting challenge for
Monte-Carlo simulations. Theories that do not have a sign problem can provide
valuable guidance and insight for physically more relevant ones that do.
Replacing the gauge group SU(3) of QCD by the exceptional group G2, for
example, leads to such a theory. It has mesons as well as bosonic and fermionic
baryons, and shares many features with QCD. This makes the G2 gauge theory
ideally suited to study general properties of dense, strongly-interacting
matter, including baryonic and nuclear Fermi pressure effects. Here we present
the first-ever results from lattice simulations of G2 QCD with dynamical
fermions, providing a first explorative look at the phase diagram of this
QCD-like theory at finite temperature and baryon chemical potential.
