Topological and Nontopological Solitons in a Gauged O(3) Sigma Model with Chern-Simons term

TheO(3) nonlinear sigma model with its U(1) subgroup gauged, where the gauge field dynamics is solely governed by a Chern-Simons term, admits both topological as well as nontopological self-dual soliton solutions for a specific choice of the potential. It turns out that the topological solitons are infinitely degenerate in any given sector. ∗ E-mail: [email protected] ∗∗ E-mail: [email protected] 1 The O(3) sigma model in 2+1 dimensions is exactly integrable [1] in the Bogomol’nyi limit [2]. The stability of these soliton solutions are guarantied by topological arguments. However, the solitons in this model, which can be expressed in terms of rational functions, are scale invariant. Due to this conformal invariance, the size of these solitons can change arbitrarily during the time evolution without costing any energy. In fact, numerical simulation of these soliton solutions indeed supports such a behaviour [3]. Naturally, the particle interpretation of these solitons upon quantization is not valid. There are several ways to break the scale invariance of this model [4,5]. Construction of Q-lumps [5] is one such example where the scale invariance is broken by including a specific potential term in the sigma model. The collapse of the soliton’s size in this model is prevented by making a rotation in the internal space of the field variables. These finite energy solitons are necessarily time-dependent with a constant angular velocity. Very recently, it was shown that the scale invariance of the O(3) sigma model can also be broken by gauging the U(1) subgroup as well as including a potential term [6]. However, in contrast to the Q-lump case, no rotation in the internal space of the scalar field variables is necessary. These soliton solutions are static with zero charge and angular momentum and though the energy is quantized, flux is not. It is worth enquiring at this point whether or not static soliton solutions with nonzero but finite charge and angular momentum is possible in any version of gauged O(3) sigma model. In this context it is worth recalling that static solitons in 2 + 1 dimensional abelian Higgs model acquire nonzero charge and angular momentum in the presence of the Chern-Simons ( CS ) term [7]. The purpose of this letter is to show that the gauged O(3) sigma model with the gauge field dynamics governed solely by a CS term indeed admits soliton solutions with broken scale invariance. To put it in another way, in gauged sigma model with pure CS term one can study the breaking of scale invariance of the