Interplay between SU (Nf) chiral symmetry, U (1)A axial anomaly, and massless bosons

The standard wisdom on the origin of massless bosons in the spectrum of a quantum field theory (QFT) describing the interaction of gauge fields coupled to matter fields is based on two well-known features: gauge symmetry and spontaneous symmetry breaking of continuous global symmetries. However, we will show in this article how the topological properties, which originate the U(1)A axial anomaly in a QFT that describes the interaction of fermion matter fields and gauge bosons, are the basis of an alternative mechanism to generate massless bosons in the chiral limit, if the non-Abelian SU(Nf)A chiral symmetry is fulfilled in the vacuum. We will also test our predictions with the results of a well-known two-dimensional model, the two-flavor Schwinger model, which was analyzed by Coleman long ago, and will give a reliable answer to some of the questions he asked himself on the spectrum of the model in the strong-coupling (chiral) limit. We will also analyze what the expectations for the U(N) gauge-fermion model in two dimensions are and will discuss the impact of our results in the chirally symmetric high-temperature phase of QCD, which was present in the early Universe and is expected to be created in heavy-ion collision experiments. To keep mathematical rigor, we perform our calculations using a lattice regularization and Ginsparg-Wilson fermions