Chiral Phase Transition and Baryon Number Conservation

In the standard $R^4$ embedding of the chiral O(4) model in 3+1 dimensions the winding number is not conserved near the chiral phase transition and thus no longer can be identified with baryon number. In order to reestablish conserved baryon number in effective low-energy models near and above the critical temperature $T_c$ it is argued that insisting in O(N) models on the angular nature of the chiral fields with fixed boundary conditions restores conservation of winding number. For N=2 in 1+1 dimensions it is illustrated that as a consequence of the angular boundary conditions nontrivial solutions exist which would be unstable in $R^2$; moving trajectories avoid crossing the origin; and time evolution of random configurations after a quench leads to quasistable soliton-antisoliton ensembles with net winding number fixed.