Exact Self-dual Soliton Solutions in a Gauged O(3) Sigma Model with Anomalous Magnetic Moment Interaction

It is shown that a gauged nonlinear O(3) sigma model with anomalous magnetic moment interaction in 2 + 1 dimensions is exactly integrable for static, self-dual field configurations. The matter fields are exactly equivalent to those of the usual ungauged nonlinear O(3) sigma model. These static soliton solutions can be mapped into an Abelian purely magnetic vortex solutions through a suitable reduction of the non-Abelian gauge group. A relativistic Abelian model in 2 + 1 dimensions is also presented where these purely magnetic vortices can be realized. ∗ E-mail: [email protected] 1 The nonlinear O(3) sigma model in 2 + 1 dimensions is popular because of its applicability in various diverse branches of physics. The soliton solutions of this model play a crucial role in most of these applications. Fortunately, all the finite energy static, self-dual soliton solutions of this model are well known which can be expressed in terms of rational functions [1]. Interestingly enough, even when the global symmetry is made local to accommodate gauge field interaction in the theory and the gauge field dynamics is solely governed by a non-Abelian Chern-Simons (CS) term, all the static, self-dual soliton solutions can be written down explicitly [2]. In particular, the matter field solutions are same for both the ungauged as well as gauged nonlinear sigma model. These static soliton solutions can be mapped into an Abelian purely magnetic vortex solutions through a suitable reduction of the non-Abelian gauge group. These magnetic vortices are exactly those found in a nonrelativistic CS theory [3] except that the solitons in the nonrelativistic theory are charged also. One can also identify these magnetic vortices as the classical solutions of an Abelian theory in two dimensional Euclidean space with a topological coupling [2]. However, no relativistic action with dynamical gauge field in 2 + 1 dimensions is known which reproduces these magnetic vortices. In general, the gauge field dynamics in 2+1 dimensions is governed by both Maxwell as well as CS term. The Maxwell term can be dropped from the action only in the long wave-length limit [4]. Thus, it is worth enquiring at this point, whether or not the gauged nonlinear O(3) sigma model with the gauge field dynamics governed by both the Maxwell and the CS term, admits static, self-dual soliton solutions. It is known from the study of vortex solutions in different Abelian as well as non-Abelian Higgs model that incorporation of anomalous magnetic moment interaction [5,6] is necessary in order to have self-dual soliton solution in presence of both the Maxwell and the CS term in the theory [7,8].