Conjecture about the QCD phase diagram

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.