Nonabelian Faddeev-Niemi Decomposition of the SU(3) Yang-Mills Theory

Faddeev and Niemi (FN) have introduced an abelian gauge theory which simulates dynamical abelianization in Yang-Mills theory (YM). It contains both YM instantons and Wu-Yang monopoles and appears to be able to describe the confining phase. Motivated by the meson degeneracy problem in dynamical abelianization models, in this note we present a generalization of the FN theory. We first generalize the Cho connection to dynamical symmetry breaking pattern SU(N+1) -> U(N), and subsequently try to complete the Faddeev-Niemi decomposition by keeping the missing degrees of freedom. While it is not possible to write an on-shell complete FN decomposition, in the case of SU(3) theory of physical interest we find an off-shell complete decomposition for SU(3) -> U(2) which amounts to partial gauge fixing, generalizing naturally the result found by Faddeev and Niemi for the abelian scenario SU(N+1) -> U(1)^N. We discuss general topological aspects of these breakings, demonstrating for example that the FN knot solitons never exist when the unbroken gauge symmetry is nonabelian, and recovering the usual no-go theorems for colored dyons.Comment: Latex 30 page

Smoothed one-core and core-multi-shell regular black holes

We discuss the generic properties of a general, smoothly varying, spherically symmetric mass distribution D(r,theta), with no cosmological term (. is a length scale parameter). Observing these constraints, we show that (1.) the de Sitter behavior of spacetime at the origin is generic and depends only on D(0,theta), (2.) the geometry may posses up to 2(k + 1) horizons depending solely on the total mass M if the cumulative distribution of D(r,theta) has 2k + 1 inflection points, and (3.) no scalar invariant nor a thermodynamic entity diverges. We define new two-parameter mathematical distributions mimicking Gaussian and step-like functions and reduce to the Dirac distribution in the limit of vanishing parameter.. We use these distributions to derive in closed forms asymptotically flat, spherically symmetric, solutions that describe and model a variety of physical and geometric entities ranging from noncommutative black holes, quantumcorrected black holes to stars and dark matter halos for various scaling values of.. We show that the mass-to-radius ratio pi c(2)/G is an upper limit for regular-black-hole formation. Core-multi-shell and multi-shell regular black holes are also derived