相关论文: Faddeev-Skyrme Model and Rational Maps
A class of exact solutions of the Faddeev model, that is, the modified SO(3) nonlinear sigma model with the Skyrme term, is obtained in the four dimensional Minkowskian spacetime. The solutions are interpreted as the isothermal coordinates…
We introduce a Skyrme type, four dimensional Euclidean field theory made of a triplet of scalar fields n, taking values on the sphere S^2, and an additional real scalar field phi, which is dynamical only on a three dimensional surface…
Faddeev and Niemi have proposed a decomposition of SU(N) Yang-Mills theory in terms of new variables, appropriate for describing the theory in the infrared limit. We extend this method to SO(2N) Yang-Mills theory. We find that the SO(2N)…
We prove that, modulo rigid motions, the Hopf map is the unique minimizer of the Faddeev--Skyrme energy in its homotopy class, provided that the radius of the target 2-sphere is not smaller than the radius of the domain 3-sphere.
We study geometric variational problems for a class of effective models in quantum field theory known as Faddeev-Skyrme models. Mathematically one considers minimizing an energy functional on homotopy classes of maps from closed 3-manifolds…
We perform full three-dimensional numerical relaxations of isospinning Hopf solitons with Hopf charge up to 8 in the Skyrme-Faddeev model with mass terms included. We explicitly allow the soliton solution to deform and to break the…
We discuss the existence of knot solitons (Hopfions) in a Skryme-Faddeev-Niemi-type model on the target space $SU(3)/U(1)^2$, which can be viewed as an effective theory of both the $SU(3)$ Yang-Mills theory and the $SU(3)$…
Skyrme theory on S^2 (Faddeev coset proposal), is analyzed with a generalization of 0-curvature integrability, based on gauge techniques. New expressions valid for models in the sphere are given. The relation of the minimum energy…
We construct new solutions of the Faddeev-Skyrme model with a symmetry breaking potential admitting $S^1$ vacuum. It includes, as a limiting case, the usual $SO(3)$ symmetry breaking mass term, another limit corresponds to the potential…
The Skyrme-Faddeev model has planar soliton solutions with target space $\mathbb{C}P^N$. An Abelian Chern-Simons term (the Hopf term) in the Lagrangian of the model plays a crucial role for the statistical properties of the solutions.…
Hopf solitons in the Skyrme-Faddeev model -- S^2-valued fields on R^3 with Skyrme dynamics -- are string-like topological solitons. In this Letter, we investigate the analogous lattice objects, for S^2-valued fields on the cubic lattice Z^3…
The variables appropriate for the infrared limit of unconstrained SU(2) Yang-Mills field theory are obtained in the Hamiltonian formalism. It is shown how in the infrared limit an effective nonlinear sigma model type Lagrangian can be…
The strongly coupled limit of the Skyrme-Faddeev-Niemi model (i.e., without quadratic kinetic term) with a potential is considered on the spacetime S^3 x R. For one-vacuum potentials two types of exact Hopf solitons are obtained. Depending…
Hopf solitons in the Skyrme-Faddeev model are string-like topological solitons classified by the integer-valued Hopf charge. In this paper we introduce an approximate description of Hopf solitons in terms of elastic rods. The general form…
The method of reduction of a non-Abelian gauge theory to the corresponding unconstrained system is exemplified for SU(2) Yang-Mills field theory. The reduced Hamiltonian which describes the dynamics of the gauge invariant variables is…
The Nicole model is a conformal field theory in three-dimensional space. It has topological soliton solutions classified by the integer-valued Hopf charge, and all currently known solitons are axially symmetric. A volume-preserving flow is…
We construct exact vortex solutions in 3+1 dimensions to a theory which is an extension, due to Gies, of the Skyrme-Faddeev model, and that is believed to describe some aspects of the low energy limit of the pure SU(2) Yang-Mills theory.…
The O(3) sigma model in two spatial dimensions admits topological (Bogomol'nyi) lower bound on its energy. This paper proposes a lattice version of this system which maintains the Bogomol'nyi bound and allows the explicit construction of…
We make progress towards a derivation of a low energy effective theory for SU(2) Yang-Mills theory. This low energy action is computed to 1-loop using the renormalization group technique, taking proper care of the Slavnov-Taylor identities…
A model of an inversion-symmetric frustrated spin system is introduced which hosts three-dimensional extensions of magnetic Skyrmions. In the continuum approximation this model reduces to a non-linear sigma model on a squashed sphere which…