We know that:
Nambu-Goldstone bosons come from Goldstone theorem: a spontaneous (continuous)-symmetry breaking of the system leads to massless scalar modes.
quantum anomaly: is the anomalous phenomena where the (classical Noether) symmetry G respected by the physical system in a classical limit, but this symmetry G is broken by the quantum effect. This is the case where the action S preserves the symmetry, but the path integral partition function Z=∫[DΨ][DΦ]…eiS and the measures [DΨ][DΦ]… do not preserves the symmetry.
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Question: whether there is any example that Nambu-Goldstone bosons can be derived from a spontaneous symmetry breaking caused by quantum anomaly effect? Alternatively, whether there is a known theorem to prove ``No Nambu-Goldstone bosons from a quantum anomaly symmetry breaking?''
[words of caution & side remark]: I offer some further thoughts if you wish you can skip it. There is a statement learned: Nambu-Goldstone bosons do not generally appear for a spontaneously broken symmetry if the relevant global symmetry is broken by the effects of the anomaly and instantons. This is regarded as a reason why we do not observe a light pseudo-scalar meson η′ in the QCD mesons. 1 among the 9 mesons is this η′, which stands for axial U(1)A anomalous symmetry breaking, there are still SU(Nflavlor)A=SU(3)A which is spontaneous broken by dynamical symmetry breaking, which induces 8 among the 9 mesons, such as three π, three κ, and one η.
There are also SU(Nflavlor)V=SU(3)V broken by the nonzero explicit quark masses(mu≠md≠ms). There is also U(1)V broken by Sphaleron, such that numebr of baryon Nbaryon is not conserved, but which only conserved numbers of Nbaryon−Nlepton. Anyway, altogether
SU(N)V×SU(N)A×U(1)V×U(1)A
makes it to be the full
U(N)V×U(N)A.
Simply that U(1)A symmetry is anomalous broken by the quantum effect, but we do not see its Goldstone boson η′.
ps. please one may read full comments below the questions.
This post imported from StackExchange Physics at 2014-06-04 11:33 (UCT), posted by SE-user Idear