We present a phase diagram study of the O(4) model as an
effective theory for 2-flavor QCD. In the chiral limit, both theories
perform spontaneous symmetry breaking with isomorphic groups,
which suggests that they belong to the same universality class.
Since we are interested in high temperature, we further assume dimensional
reduction to the 3d O(4) model, which implies topological sectors.
According to Skyrme and others, the corresponding topological charge
represents the baryon number. Hence the baryon chemical
potential $\mu_{B}$ appears as an imaginary vacuum angle, which can
be included in the lattice simulations without any sign problem.
We present simulation results for the critical line in the chiral
limit, and for the crossover in the presence of light quark masses.
The shapes of these lines are compatible with other conjectures, but
up to about $\mu_{B} \approx 300$~MeV we do not find a Critical Endpoint,
although there are indications for it to be near-by.