Instantons, vortices and confinement in SU(2) Yang-Mills theory

Full text: In this work, we derive a recently proposed Abelian model to describe the interaction of correlated instantons, center vortices, and dual fields in three dimensional SU(2) Yang-Mills theory. Correlated monopoles and center vortices are believed to play a relevant role in accommodating the different properties of the confining string in Yang-Mills theories, receiving support from lattice simulations. In fact, scenarios based on either monopoles or closed center vortices are only partially successful to describe the expected behavior of the potential between quarks. At asymptotic distances, this potential should be linear and depend on the representation of the subgroup Z(N) of SU(N) (N-ality). At intermediate scales, it should posses Casimir scaling. The Cho-Faddeev- Niemi representation (CFN) can be used to associate monopoles with defects of the local color frame used to decompose the gauge fields. This possible frame defects can be extended to describe not only monopoles but also center vortices, correlated or not. In these scenarios, one of the difficulties is how to deal with the integration over an ensemble of extended objects, after considering a phenomenological parametrization of their properties, such as stiffness, interactions with dual fields, and interactions between them. This is particularly severe in four dimensional theories where center vortices generate two dimensional extended world surfaces. However, in three dimensions center vortices are stringlike and an ensemble of world lines is naturally associated with a second quantized field theory. The aim of this work is presenting a careful derivation of an effective model, considering instantons and center vortices in D=3 SU(3) theory, after parameterizing some intrinsic physical properties that these objects could present. One of the fundamental ingredients will be the adoption of recent techniques borrowed from polymer physics, where the extended objects are also one dimensional. This model corresponds to a generalization of the t' Hooft model; it includes a coupling with the dual field that can be defined in order to represent the off-diagonal sector. This coupling is essential to relate the possible vortex phases with enabled or disabled large dual transformations, and discuss in this framework the observability of Wilson surfaces. (author)