Topological Insulators Avoid the Parity Anomaly

Understand

The surface of a 3+1d topological insulator hosts an odd number of gapless Dirac fermions when charge conjugation and time-reversal symmetries are preserved.

• Viewed as a purely 2+1d system, this surface theory would necessarily explicitly break parity and time-reversal when coupled to a fluctuating gauge field.
• Here we explain why such a state can exist on the boundary of a 3+1d system without breaking these symmetries, even if the number of boundary components is odd.
• This is accomplished from two complementary perspectives: topological quantization conditions and regularization.