Anomalies of discrete symmetries in theories of Weyl fermions

Weyl fermions, which are massless fermions with a definite chirality, are thought of as a building block for fermions in quantum field theory. They are not only proposed as fundamental particles in nature (though not observed yet) but can be realized as emergent quasiparticles in a low-energy condensed matter system, such as Weyl semimetals and Weyl superconductors. As Weyl fermions are chiral, symmetries acting on them in a chiral way might be anomalous. While anomalies of Weyl fermions with continuous symmetries like U(1) have been well understood, the cases of discrete symmetries have been studied much less. In this talk, I will discuss anomalies of discrete symmetries in theories of Weyl fermions, and address some possible applications in condensed matter systems.