2018/08/08 by Hsieh, Chang-Tse · 3 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.1808.02881
We revisit discrete gauge anomalies in chiral fermion theories in 3+1 dimensions. We focus on the case that the full symmetry group of fermions is Spin(4)×ℤn or (Spin(4)×ℤ2m)/ℤ2 with ℤ2 being the diagonal ℤ2 subgroup. The anomalies are determined by the consistency condition --- based on the Dai-Freed theorem --- of formulating a chiral fermion theory on a generic spacetime manifold with a structure associated with either one of the above symmetry groups and are represented by elements of some finite abelian groups. Accordingly, we give a reformulation of the anomaly cancellation conditions, and compare them with the previous result by Ibáñez and Ross. The role of symmetry extensions in discrete symmetry anomalies is clarified in a formal fashion. We also study gapped states of fermion with an anomalous global ℤn symmetry, and present a model for constructing these states in the framework of weak coupling.