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The standard wisdom on the origin of massless bosons in the spectrum of aQuantum Field Theory $(QFT)$ describing the interaction of gauge fields coupledto matter fields is based on two well known features: gauge symmetry, andspontaneous symmetry breaking of continuous global symmetries. However we willshow in this article how the topological properties, that originate the$U(1)_A$ axial anomaly in a $QFT$ which describes the interaction of fermionmatter fields and gauge bosons, are the basis of an alternative mechanism togenerate massless bosons in the chiral limit, if the non-abelian $SU(N_f)_A$chiral symmetry is fulfilled in the vacuum. We will also test our predictionswith the results of a well known two-dimensional model, the two-flavourSchwinger model, which was analyzed by Coleman long ago, and will give areliable answer to some of the questions he asked himself on the spectrum ofthe model in the strong-coupling (chiral) limit. We will also analyze what arethe expectations for the $U(N)$ gauge-fermion model in two dimensions, and willdiscuss on the impact of our results in the chirally symmetric high temperaturephase of $QCD$, which was present in the early universe, and is expected to becreated in heavy-ion collision experiments.

Interplay between $SU(N_f)$ chiral symmetry, $U(1)_A$ axial anomaly and massless bosons