An Effective Dual Abelian-Higgs Model from SU(2) Yang-Mills theory via Connection Decomposition

Abstract

It has long argued that confinement in non-Abelian gauge theories, such as QCD, can be account for by analogy with typed II superconductivity. In this paper, we show that it is possible to arrive at an effective dual Abelian-Higgs model, the dual and relativistic version of Ginzburg-Landau model for superconductor, from SU(2) Yang-Mills theory based on the Faddeev-Niemi connection decomposition and the order-disorder assumptions for the gauge field. The implication of these assumptions is discussed and role of the resulted scalar field is analyzed associated with the "electric-magnetic" duality and theory vacuum. It is shown that the mass generation of the gauge vector field can arise from quantum fluctuation of the coset basis variable $\partial \mathbf{n}$, and the mass of the "electric" field is approximately equal to that of the scalar particle. A generalized dual London equation with topologically quantized singular vortices is derived for the static "electric" field from the our dual model.