An effective action for monopoles and knot solitons in Yang-Mills theory

By comparision with numerical results in the maximal Abelian projection of lattice Yang-Mills theory, it is argued that the nonperturbative dynamics of Yang Mills theory can be described by a set of fields that take their values in the coset space SU(2)/U(1). The Yang-Mills connection is parameterized in a special way to separate the dependence on the coset field. The coset field is then regarded as a collective variable, and a method to obtain its effective action is developed. It is argued that the physical excitations of the effective action may be knot solitons. A procedure to calculate the mass scale of knot solitons is discussed for lattice gauge theories in the maximal Abelian projection. The approach is extended to the SU(N) Yang-Mills theory. A relation between the large N limit and the monopole dominance is pointed out.Comment: plain Latex, 12 pages, no figures, a few references and comments are added, a final version for Phys. Lett.

Decomposing the Yang-Mills Field

Recently we have proposed a set of variables for describing the physical parameters of SU(N) Yang--Mills field. Here we propose an off-shell generalization of our Ansatz. For this we envoke the Darboux theorem to decompose arbitrary one-form with respect to some basis of one-forms. After a partial gauge fixing we identify these forms with the preimages of holomorphic and antiholomorphic forms on the coset space $SU(N)/U(1)^{N-1}$, identified as a particular coadjoint orbit. This yields an off-shell gauge fixed decomposition of the Yang-Mills connection that contains our original variables in a natural fashion.Comment: 5 pages, latex, no figure

Spin-Charge Separation, Conformal Covariance and the SU(2) Yang-Mills Theory

In the low energy domain of four-dimensional SU(2) Yang-Mills theory the spin and the charge of the gauge field can become separated from each other. The ensuing field variables describe the interacting dynamics between a version of the O(3) nonlinear $\sigma$-model and a nonlinear Grassmannian $\sigma$-model, both of which may support closed knotted strings as stable solitons. Lorentz transformations act projectively in the O(3) model which breaks global internal rotation symmetry and removes massless Goldstone bosons from the particle spectrum. The entire Yang-Mills Lagrangian can be recast into a generally covariant form with a conformally flat metric tensor. The result contains the Einstein-Hilbert Lagrangian together with a nonvanishing cosmological constant, and insinuates the presence of a novel dimensionfull parameter in the Yang-Mills theory.Comment: some misprints in equations correcte

An alternative interpretation of the Weinberg-Salam model

A problem of mass generation in the Unified EM+W theory is discussed. Two hypothetical possibilities for the nature of Higgs field are proposed.Comment: Talk at the conference "New Trends in High Energy Physics", Yalta, Crimea, Sept.27-Oct.4 2008; v2: added address, one formula and several misprints were correcte

Noncommutative Hypergeometry

A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.Comment: 14 pages, LaTeX (amsart

Three Dimensional Gravity From SU(2) Yang-Mills Theory in Two Dimensions

We argue that two dimensional classical SU(2) Yang-Mills theory describes the embedding of Riemann surfaces in three dimensional curved manifolds. Specifically, the Yang-Mills field strength tensor computes the Riemannian curvature tensor of the ambient space in a thin neighborhood of the surface. In this sense the two dimensional gauge theory then serves as a source of three dimensional gravity. In particular, if the three dimensional manifold is flat it corresponds to the vacuum of the Yang-Mills theory. This implies that all solutions to the original Gauss-Codazzi surface equations determine two dimensional integrable models with a SU(2) Lax pair. Furthermore, the three dimensional SU(2) Chern-Simons theory describes the Hamiltonian dynamics of two dimensional Riemann surfaces in a four dimensional flat space-time

Relaxation of twisted vortices in the Faddeev-Skyrme model

We study vortex knotting in the Faddeev-Skyrme model. Starting with a straight vortex line twisted around its axis we follow its evolution under dissipative energy minimization dynamics. With low twist per unit length the vortex forms a helical coil, but with higher twist numbers the vortex becomes knotted or a ring is formed around the vortex.Comment: 7 pages, 8 jpg figure