MASSLESSNESS OF PHOTON AND CHERN-SIMONS TERM IN (2 + 1)-DIMENSIONAL QED

Abstract

We study the realization of global symmetries in (2 + 1)-dimensional QED with two fermion flavors. It is shown that, in a certain range of mass parameters, the chiral symmetry [Formula: see text] and the flux symmetry Φ = ∫d2xB are both spontaneously broken, but the combination I = Q5 − sign (m)e/πΦ remains unbroken. The photon is identified with the corresponding massless excitation, which is required in this case by Goldstone theorem. An order parameter vanishes and chiral and flux symmetries are realized in the Kosterlitz-Thouless mode. Outside this range of parameters the vacuum is symmetric and simultaneously the photon's topological mass is generated. Similar symmetry breaking pattern U (1) ⊗ U (1) → U (1) is realized in Chern-Simons electrodynamics for a particular value of the bare CS-term coefficient at which the "statistical photon" becomes massless. We point out the direct correspondence of this model to the superconducting anyon gas.