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

Abstract

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.

Latex 30 pages

References in corpus (4)

• Non-Abelian duality from vortex moduli: a dual model of color-confinement
• A Faddeev-Niemi Solution that Does Not Satisfy Gauss' Law
• On Solutions to the "Faddeev-Niemi" Equations
• On Confinement Index

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• Confinement and duality in supersymmetric gauge theories
• Skyrme and Faddeev models in the low-energy limit of 4d Yang-Mills-Higgs theories
• Reformulations of Yang-Mills Theories with Space-time Tensor Fields
• New Faddeev-Niemi type variables for static SU(3) Yang-Mills theory