Chern-Simons Term and Charged Vortices in Abelian and Nonabelian Gauge Theories

Abstract

In this article we review some of the recent advances regarding the charged vortex solutions in abelian and nonabelian gauge theories with Chern-Simons (CS) term in two space dimensions. Since these nontrivial results are essentially because of the CS term, hence, we first discuss in some detail the various properties of the CS term in two space dimensions. In particular, it is pointed out that this parity (P) and time reversal (T) violating but gauge invariant term when added to the Maxwell Lagrangian gives a massive gauge quanta and yet the theory is still gauge invariant. Further, the vacuum of such a theory shows the magneto-electric effect. Besides, we show that the CS term can also be generated by spontaneous symmetry breaking as well as by radiative corrections. A detailed discussion about Coleman-Hill theorem is also given which aserts that the parity-odd piece of the vacuum polarization tensor at zero momentum transfer is unaffected by two and multi-loop effects. Topological quantization of the coefficient of the CS term in nonabelian gauge theories is also elaborated in some detail. One of the dramatic effect of the CS term is that the vortices of the abelian (as well as nonabelian) Higgs model now acquire finite quantized charge and angular momentum. The various properties of these vortices are discussed at length with special emphasis on some of the recent developments including the discovery of the self-dual charged vortex solutions.