Cancellation of gauge anomalies is a fundamental constraint on a consistent quantum field theory. While anomalies of continuous symmetries such as U(1) are well understood, the cases of discrete symmetries have been studied much less. In this talk, we revisit discrete gauge anomalies in chiral fermion theories in 3 + 1 dimensions, from a more modern perspective based on the concept of symmetry-protected topological phases. We focus on the simplest case that the discrete internal symmetries are cyclic groups. A reformulation of the "discrete anomaly cancellation" conditions, first proposed by Ibáñez and Ross in 1991 [1], is given. Also, the role of symmetry extensions in discrete anomalies is clarified in a formal fashion, respecting the viewpoint in the work of Banks and Dine [2]. Therefore, our work provides a fundamental understanding of discrete symmetry anomalies, (This talk is based on a recent arXiv preprint [3].)

References:
[1] L. E. Ibáñez and G. G. Ross, Phys. Lett. B 260 (1991) 291.
[2] T. Banks and M. Dine, Phys. Rev. D 45 (1992) 1424.
[3] C.-T. Hsieh, arXiv:1808.02881 (2018).