Critical Generation of Soliton Mode in a Gauged O(3) Sigma Model with Interpolating Potential


We show that a new soliton mode is generated in a gauged sigma model with interpolating potential when the interpolation parameter decreases below a critical value. Recently a class of gauged O(3) sigma models in three dimensions have been studied [1, 2, 3, 4, 5] where a U(1) subgroup of the O(3) symmetry of the model was gauged by coupling the sigma model fields with a gauge field through the corresponding U(1) current. This is different from the minimal coupling via the topological current discussed previously [6]. The motivation behind the new gauged O(3) sigma models was to break the scale invariance of the self dual solutions of the usual O(3) sigma model [7]. Initially the gauge field dynamics was assumed to be dictated by the Maxwell term [1]. Later the extension of the model with the Chern Simons coupling was investigated [2]. A particular form of self interaction was required to be included in these models in order to saturate the Bogomol’nyi bounds [8]. The form of the assumed self interaction potential is of crucial importance. The minima of the potential determine the vaccum structure of the theory. The solutions change remarkably when the vaccum structure exhibits spontaneous breaking of the symmetry of the gauge group. Thus it was demonstrated that the observed degeneracy of the solutions of [1, 2] is lifted when potentials with symmetry breaking minima were incorporated [4, 5]. A generalisation of the models [1, 2] was proposed in [3]where an adjustable real parameter v was introduced in the expression of the self interaction potential. Detailed solutions of the model with the C S coupling were provided. The parameter v interpolates between the symmetric and symmetry breaking phases. The inclusion of such adjustable potential in the corresponding Maxwell coupled model was conjectured, but not fully explored. In this letter we show that this generalisation indeed leads to certain important consequences. The most interesting outcome is a kind of ’critical phenomenon’ where a new self dual soliton mode emerges when the parameter v decreases below v = 1. It will be useful to start with a brief review of the nonlinear O(3) sigma model [7]. The lagrangian of the model is given by, L = 1 2 ∂μφ · ∂ φ (1) Here φ is a triplet of scalar fields constituting a vector in the internal space with unit norm φa = na · φ, (a = 1, 2, 3) (2) φ · φ = φaφa = 1 (3) The vectors na constitute a basis of unit orthogonal vectors in the internal space. We work in the Minkowskian space time with the metric tensor diagonal, gμν = (1,−1,−1). The finite energy solutions of the model (1) satisfies the boundary condition limφ = φa(0) (4) at physiacal infinity. The condition (4) corresponds to one point compactification of the physical infinity. The physical space R2 becomes topologically equivalent to S2 due to this compactification. The static finite energy solutions of the model are then maps from this sphere to the internal sphere. Such solutions are classified by the homotopy [9]

Cite this paper

@inproceedings{Mukherjee1999CriticalGO, title={Critical Generation of Soliton Mode in a Gauged O(3) Sigma Model with Interpolating Potential}, author={Pradip Mukherjee}, year={1999} }