Gauged Sigma Models Research Articles

Solitons in (1+1)-dimensional gauged σ models

We study soliton solutions in 1+1 dimensional gauged sigma models, obtained by dimensional reduction from its 2+1 dimensional counterparts. We show that the Bogomol'nyi bound of these models can be expressed in terms of two conserved charges in a similar way to that of the BPS dyons in 3+1 dimensions. Purely magnetic vortices of the 2+1 dimensional completely gauged sigma model appear as charged solitons in the corresponding 1+1 dimensional theory. The scale invariance of these solitons is also broken because of the dimensional reduction. We obtain exact static soliton solutions of these models saturating the Bogomol'nyi bound.

2D topological solitons in the gauged easy-axis Heisenberg antiferromagnet model

Field equations of the 3-component U(1) gauged sigma model (“the A3M model”) with spontaneously broken Z (2) symmetry are presented for ( D + 1)-dimensional space-time. Localized solutions of the two-dimensional A3M model with the unit topological charge are found numerically; these topological solitons describe (at least for small values of a parameter p, p < p 0) stable bound states of the unit 3-component “easy-axis” Heisenberg field and the Maxwell field. Possible physical implications of 2D and 3D topological solitons of the A3M model are discussed.

The existence of solitons in gauged sigma models with broken symmetry: Some remarks

We prove the existence of multisolitons in the gauged self-dual Maxwell and Chern–Simons sigma models with broken symmetry. In the context of topological solutions, the existence proofs rely on established results on earlier models. In the context of nontopological solutions with radial symmetry, the proof is by adapting a shooting argument.

A necessary and sufficient condition for the existence of multisolitons in a self-dual gauged sigma model

This paper presents a resolution of the gaugedO(3) sigma model proposed by B.J. Schroers in which the matter field ø mapsR 2 intoS 2 while the vector gauge potential gives rise to a magnetic field. It is shown that for each natural numberN there are solutions to saturate the classical energy lower boundE≧4πN for the field configurations in the topological family deg(ø)=N if and only ifN≠1. Furthermore the solutions obtained depend on at least 4N−3 continuous parameters, the associated magnetic flux can assume its value in an open interval, and the decay rates of the field strengths may be specified in a suitable range. These solutions are multisolitons represented byN prescribed lumps of the magnetic field, simulatingN identical particles in equilibrium, and are governed by a nonlinear elliptic equation with both vortex and anti-vortex source terms.

Solitons in gauged Sigma models: 2 dimensions

A prescription for the gauging of 2-dimensional Sigma models is studied. This prescription satisfies the criterion that the U(1) gauged Sigma model supports topologically stable solitons, like its ungauged counterpart. The gauging is carried out separately for both Maxwell and Chern-Simons dynamics of the U(1) field and it is shown that independently of this dynamics and of the inclusion of all possible Skyrme terms, our criterion is fulfilled. In the Maxwell case, the vortices are presented in detail and are seen to have some interesting properties of their own.

Superconformal sigma models in higher than two dimensions

Rigidly superconformal sigma models in higher than two dimensions are constructed. These models rely on the existence of conformal Killing spinors on the ( p + 1)-dimensional worldvolume ( p ⩽ 5), and homothetic conformal Killing vectors in the d-dimensional target space. In the bosonic case, substituting into the action a particular form of the target space metric admitting such Killing vectors, we obtain an action with mainfest worldvolume conformal symmetry, which describes the coupling of d − 1 scalars to a conformally flat metric on the worldvolume. We also construct gauged sigma models with worldvolume conformal supersymmetry. The models considered here are generalizations of the singleton actions on S P × S 1, constructed some time ago by Nicolai and these authors.

Bogomolny-type equations for gravitating gauged sigma models

It is shown that the complete set of field equations of a gauged sigma model coupled to gravity is satisfied by a set of first-order equations when the metric is static.

SYMMETRIES OF p-BRANES

Using canonical methods, we study the invariance properties of a bosonic p-brane propagating in a curved background locally diffeomorphic to M×G, where M is space-time and G a group manifold. The action is that of a gauged sigma model in p+1 dimensions coupled to a Yang-Mills field and a (p+1) form in M. We construct the generators of Yang-Mills and tensor gauge transformations and exhibit the role of the (p+1) form in canceling the potential Schwinger terms. We also discuss the Noether currents associated with the global symmetries of the action and the question of the existence of infinite-dimensional symmetry algebras, analogous to the Kac-Moody symmetry of the string.

Higher spin, W and gauge symmetries in two-dimensional sigma models

The classical higher spin symmetries of bosonic and supersymmetric gauged sigma models are examined. The necessary and sufficient conditions for the invariance of the action of a gauged sigma model under a higher spin transformation are derived and the commutator of two such symmetries is presented. In particular, the W symmetries of a gauged sigma model without Wess-Zumino term and a gauged Wess-Zumino-Witten model are examined.