文档介绍：On the large N limit, Wilson Loops, Confinement and
Composite Antisymmetric Tensor Field theories
Carlos Castro
Center for Theoretical Studies of Physical Systems
Clark Atlanta University, Atlanta, GA. 30314
April 2002, Revised February 2004
Abstract
A novel approach to evaluate the Wilson loops asociated 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 ofthe 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 containthe 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.
I. Introduction
It has been believed for a long time that QCD confinement is supposed to be a non-perturbative solution
to QCD in four dimensions ; to SU(3) Yang-Mills theory [ 1 ] . A formal proof of the colour confinement
amounts to a derivation of the area-law for a Wilson loop associated, for example, with the world lines of