Dirac fermion duality and the parity anomaly

摘要

We present a derivation of the recently discovered duality between the free massless (2 + 1)-dimensional Dirac fermion and QED(3). Our derivation is based on a regularized lattice model of the Dirac fermion and is similar to the more familiar derivation of the boson-vortex duality. It also highlights the important role played by the parity anomaly, which is somewhat less obvious in other discussions of this duality in the literature.