4,653 research outputs found

### 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

### 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.

### 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

### Aspects of Electric and Magnetic Variables in SU(2) Yang-Mills Theory

We introduce a novel decomposition of the four dimensional SU(2) gauge field.
This decomposition realizes explicitely a symmetry between electric and
magnetic variables, suggesting a duality picture between the corresponding
phases. It also indicates that at large distances the Yang-Mills theory
involves a three component unit vector field, a massive Lorentz vector field,
and a neutral scalar field that condenses which yields the mass scale. Our
results are consistent with the proposal that the physical spectrum of the
theory contains confining strings which are tied into stable knotted solitons.Comment: we have made substantial improvement

### Chirality and fermion number in a knotted soliton background

We consider the coupling of a single Dirac fermion to the three component
unit vector field which appears as an order parameter in the Faddeev model.
Classically, the coupling is determined by requiring that it preserves a
certain local frame independence. But quantum mechanically the separate left
and right chiral fermion number currents suffer from a frame anomaly. We employ
this anomaly to compute the fermion number of a knotted soliton. The result
coincides with the self-linking number of the soliton. In particular, the
anomaly structure of the fermions relates directly to the inherent chiral
properties of the soliton. Our result suggests that interactions between
fermions and knotted solitons can lead to phenomena akin the Callan-Rubakov
effect

### 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

### 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

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