There are two different kinds of symmetry breaking involved in your question. The first would be spontaneous symmetry breaking. In this case we are dealing with a theory that is invariant under a certain symmetry group, but its vacuum is not. The breaking of the symmetry corresponds to a specific choice of the vacuum, the freedom of choosing a vacuum results in a new degree of freedom: the Nambu-Goldstone- boson. Depending on the type of symmetry that is broken, one might get one or more of them. In the case of the chiral symmetry of QCD, the $SU(N_f)_A$ part is broken spontaneously, resulting in eight massless bosons. The other axial part, $U(1)_A$, however, is not broken spontaneously.

The second kind of symmetry breaking would be induced by quantum anomalies. We speak of such an anomaly when a theory is classically invariant under a certain symmetry operation but the corresponding quantum theory is not. In terms of the path integral formalism this is manifest in the fact that the measure transforms in a nontrivial way. An example would be the breaking of the axial $U(1)_A$ part of the chiral symmetry in QCD, which is not related to any choice of a vacuum, and there is no Nambu-Goldstone boson connected to it. In fact, it can be traced back to something entirely different, namely instantons. The occurence of an anomaly is related to the number of fermionic zero modes of the theory: the difference between fermionic and antifermionic zero modes is given by the Pontryagin number of the topological instanton configuration of the gauge fields. This is also known as the Atiyah-Singer theorem.

Since these two possible symmetry breaking mechanism are quite distinct, the concept of Nambu-Goldstone bosons arising from quantum anomalies can only be a result of sloppy, non-standard terminology.

There are two different kinds of symmetry breaking involved in your question. The first would be spontaneous symmetry breaking, in which case we are dealing with a theory that is invariant under a certain symmetry group, but its vacuum is not. The breaking of the symmetry corresponds to a specific choice of the vacuum, the freedom of choosing a vacuum results in a new degree of freedom: the Nambu-Goldstone- boson. Depending on the type of symmetry that is broken, one might get one or more of them. In the case of the chiral symmetry of QCD, the $SU(N_f)_A$ part is broken spontaneously, resulting in eight massless bosons. The other axial part, $U(1)_A$, however, is not broken spontaneously.

The second kind of symmetry breaking would be induced by quantum anomalies. We speak of such an anomaly when a theory is classically invariant under a certain symmetry operation but the corresponding quantum theory is not. In terms of the path integral formalism this is manifest in the fact that the measure transforms in a nontrivial way. An example would be the breaking of the axial $U(1)_A$ part of the chiral symmetry in QCD, which is not related to any choice of a vacuum, and there is no Nambu-Goldstone boson connected to it. In fact, it can be traced back to something entirely different, namely instantons. The occurence of an anomaly is related to the number of fermionic zero modes of the theory: the difference between fermionic and antifermionic zero modes is given by the Pontryagin number of the topological instanton configuration of the gauge fields. This is also known as the Atiyah-Singer theorem.

Since these two possible symmetry breaking mechanism are quite distinct, the concept of Nambu-Goldstone bosons arising from quantum anomalies can only be a result of sloppy, non-standard terminology.

There are two different kinds of symmetry breaking involved in your question. The first would be spontaneous symmetry breaking. In this case we are dealing with a theory that is invariant under a certain symmetry group, but its vacuum is not. The breaking of the symmetry corresponds to a specific choice of the vacuum, the freedom of choosing a vacuum results in a new degree of freedom: the Nambu-Goldstone- boson. Depending on the type of symmetry that is broken, one might get one or more of them. In the case of the chiral symmetry of QCD, the $SU(N_f)_A$ part is broken spontaneously, resulting in eight massless bosons. The other axial part, $U(1)_A$, however, is not broken spontaneously.

The second kind of symmetry breaking would be induced by quantum anomalies. We speak of such an anomaly when a theory is classically invariant under a certain symmetry operation but the corresponding quantum theory is not. In terms of the path integral formalism, this is manifest in the fact that the measure transforms in a nontrivial way. An example would be the breaking of the axial $U(1)_A$ part of the chiral symmetry in QCD, which is not related to any choice of a vacuum, and there is no Nambu-Goldstone boson connected to it. In fact, it can be traced back to something entirely different, namely instantons. The occurence of an anomaly is related to the number of fermionic zero modes of the theory: the difference between fermionic and antifermionic zero modes is given by the Pontryagin number of the topological instanton configuration of the gauge fields. This is also known as the Atiyah-Singer theorem.

Since these two possible symmetry breaking mechanism are quite distinct, the concept of Nambu-Goldstone bosons arising from quantum anomalies can only be a result of sloppy, non-standard terminology.

There are two different kinds of symmetry breaking involved in your question. The first would be spontaneous symmetry breaking. In this case we are dealing with a theory that is invariant under a certain symmetry group, but its vacuum is not. The breaking of the symmetry corresponds to a specific choice of the vacuum, the freedom of choosing a vacuum results in a new degree of freedom: the Nambu-Goldstone- boson. Depending on the type of symmetry that is broken, one might get one or more of them. In the case of the chiral symmetry of QCD, the $SU(N_f)_A$ part is broken spontaneously, resulting in eight massless bosons. The other axial part, $U(1)_A$, however, is not broken spontaneously.

The second kind of symmetry breaking would be induced by quantum anomalies. We speak of such an anomaly when a theory is classically invariant under a certain symmetry operation but the corresponding quantum theory is not. In terms of the path integral formalism this is manifest in the fact that the measure transforms in a nontrivial way. An example would be the breaking of the axial $U(1)_A$ part of the chiral symmetry in QCD, which is not related to any choice of a vacuum, and there is no Nambu-Goldstone boson connected to it. In fact, it can be traced back to something entirely different, namely instantons. The occurence of an anomaly is related to the number of fermionic zero modes of the theory: the difference between fermionic and antifermionic zero modes is given by the Pontryagin number of the topological instanton configuration of the gauge fields. This is also known as the Atiyah-Singer theorem.

Since these two possible symmetry breaking mechanism are quite distinct, the concept of Nambu-Goldstone bosons arising from quantum anomalies can only be a result of sloppy, non-standard terminology.