ON THE LARGE N LIMIT, WILSON LOOPS, CONFINEMENT AND COMPOSITE ANTISYMMETRIC TENSOR FIELD THEORIES

Abstract

A novel approach to evaluate the Wilson loops associated with a SU (∞) 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 worldsheet 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 arbitrary rank which couple to p-branes of different dimensionality.