The supersymmetric extension of the Faddeev model

Abstract

We study the supersymmetric extension of the Faddeev model in four dimensions. The Faddeev model contains three dimensional soliton solutions and we are interested in how these solitons are affected by supersymmetry. We consider both the N = 1 and N = 2 extensions and find that in neither case it is possible to supersymmetrize the model without adding additional bosonic terms. There are essentially two ways of constructing the supersymmetric theory, one that will lead to a model which allows for solitons and another that gives a model where solitons are excluded.The N = 2 model is studied since extending supersymmetry is the natural way of including topological charges in the algebra. A lower bound to the mass is obtained by computing the central charge. The result is that it is possible to have a non-trivial lower bound on the mass, this in principle allows for massive solitons.

Extended supersymmetry and BPS solutions in baby Skyrme models

“…An N = 2 supersymmetric theory in d = 2 + 1 dimensions leads in a natural way to an N = 1 theory in one dimension higher, i.e., in d = 3 + 1 dimensions. For the Skyrme-Faddeev-Niemi (SFN) model (same field content and lagrangian as the baby Skyrme model, but in d = 3 + 1), we conclude that we cannot find an N = 1 extension with our methods, in agreement with the findings of [53,54]. On the other hand, for the restricted or extreme SFN model consisting of the quartic term and a potential only, we…”

Supersymmetrickfield theories and defect structures

“…To the best of our knowledge, the problem of supersymmetric extensions was first investigated in relation to the Skyrme model [36], which is one of the best-known theories supporting topological solitons and possessing a nonstandard kinetic term. Concretely, the supersymmetric extensions of a S 2 (or CP (1)) restriction of the Skyrme model (the so-called Skyrme-Faddeev-Niemi (SFN) model [37]) were investigated in [38] and in [39]. In both papers, a formulation of the SFN model was used where the CP (1) restriction of the Skyrme model is achieved via a gauging of the third, unwanted degree of freedom.…”

Non-Abelian Vortex-String Dynamics From Nonlinear Realization

“…There is the other independent fourth order term [46,47,48] which is simply the kinetic term squared: .5) This term arises when one constructs the low energy effective theory of pure SU (2) Yang-Mills theory [46]. It is also needed for supersymmetric generalization of the Skyrme-Faddeev term [48].…”

“…There is the other independent fourth order term [46,47,48] which is simply the kinetic term squared: .5) This term arises when one constructs the low energy effective theory of pure SU (2) Yang-Mills theory [46]. It is also needed for supersymmetric generalization of the Skyrme-Faddeev term [48]. The kinetic term becomes ∂ a Φ∂ a Φ * (1 + |Φ| 2 ) 2 = 1 2 ∂ a n · ∂ a n, (A.10) and the field strength can be rewritten as .11) Therefore the Skyrme-Faddeev term and the other four derivative term become F 2 ab = (n · ∂ a n × ∂ b n) 2 = (∂ a n × ∂ b n) 2 , (A.12) (∂ a Φ∂ a Φ * )…”