Dr. Chang-Tse Hsieh (Kavli IPMU, ISSP)
"Discrete gauge anomalies revisited"
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 (SPT) 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 Ibanez
and Ross in 1991 [1], is given. Also, the role of symmetry extensions in
discrete anomalies is clarified in a formal fashion. Therefore, our work
provides a fundamental and complete understanding of discrete symmetry
anomalies, respecting the viewpoint in the work of Banks and Dine [2].
(This talk is based on a recent arXiv preprint [3].)
References:
[1] L. E. Ibanez 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).