Parity Anomaly and Duality Web

Understand

We review the parity anomaly and a duality web in 2+1 dimensions.

• An odd dimensional non-interacting Dirac fermion theory is not parity invariant at quantum level.
• We demonstrate the parity anomaly in a three dimensional non-interacting Dirac fermion theory and a one dimensional non-interacting Dirac fermion theory.
• These theories can generate non-gauge invariant Abelian Chern-Simons terms at a finite temperature through an effective action.