On the large N limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field theories

A novel approach to evaluate the Wilson loops asociated with a $ SU ( \infty )$ gauge theory in terms of pure string degrees of freedom is presented. It is based on the Guendelman-Nissimov-Pacheva formulation of composite antisymmetric tensor field theories of area (volume ) preserving diffeomorphisms which admit $p$-brane solutions and which provide a $new$ route to scale symmetry breaking and confinement in Yang-Mills theory. The quantum effects are discussed and we evaluate the vacuum expectation values (vev) of the Wilson loops in the large $N$ limit of the $quenched$ reduced $SU(N)$ Yang-Mills theory in terms of a path integral involving pure string degrees of freedom. The $quenched$ approximation is necessary to avoid a crumpling of the string world-sheet giving rise to very large Hausdorff dimensions as pointed out by Olesen. The approach is also consistent with the recent results based on the AdS/CFT correspondence and dual QCD models (dual Higgs model with dual Dirac strings ). More general Loop wave equations in C-spaces ( Clifford manifolds ) are proposed in terms of generalized holographic variables that contain the dynamics of an aggregate of closed branes ( $ p$-loops ) of various dimensionalities. This allows us to construct the higher-dimensional version of Wilson loops in terms of antisymmetric tensor fields of arbitray rank which couple to $p$-branes of different dimensionality.