Knot Solitons
نویسنده
چکیده
The existence of ring-like and knotted solitons in O(3) non-linear σ model is analysed. The role of isotopy of knots/links in classifying such solitons is pointed out. Appearance of torus knot solitons is seen. †[email protected]; [email protected] †† permanent address Introduction: Recently the possible existence of knotlike solitons in nonlinear field theories has been argued[1, 2]. The toroidal solitons have been studied in 3-d field theories for the past two decades[3, 4, 5]. Several numerical attempts using various ansatzes have been made to study these solitons[6, 7]. There also exists contradicting results regarding the ringlike nature of the solitons for low values of topological quantum numbers[8]. The exciting possibilty of the Nonabelian gauge theories being described by new variables which will have the component of nonlinear sigma model have been pointed out[2]. This will lead to presence of exotic solitons and new applications in QCD. In this letter we point out the arguments in favor of knotted solitons and ways of chracterising them, in the specific well studied O(3) sigma model. We point out that solitons in this model are characterised in addition to the Hopf number also by the genus of the seifert surface for the torus knot. We also point out only torus knots appear in these models. The O(3) nonlinear sigma model in 3 + 1 dimensions is defined by a vector field n at every point in the space. The configuration space of the systemis characterised by maps from R −→ S. The action can be written as
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