Saturday, November 14, 2015

mathematical physics - axial anomaly for adjoint fermion v.s. fundamental fermion


It is known that the axial anomaly (chiral anomaly, the left L- right R) shows that $U(1)_A$-axial symmetry is not a global symmetry at quantum level.


In particular, one can consider the (1) fundamental fermion and (2) adjoit fermion for QCD. The $U(1)_A$-axial symmetry is not a symmetry for both cases, but there are discrete sectors that survive as a symmetry within $U(1)_A$.



What are the remained discrete axial symmetries for (1) fundamental fermion and (2) adjoint fermion, say for a Lie group G (like SU(N))?




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