On the Large N Limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field Theories

Abstract

It is shown that the large N limit of SU (N ) YM in curved m-dim backgrounds can be subsumed by a higher m + n dimensional gravitational theory which can be identified to an m-dim generally invariant gauge theory of diffs N , where N is an n-dim internal space ( Cho, Sho, Park, Yoon ). Based on these findings, a very plausible geometrical interpretation of the AdS/CF T correspondence could be given. Conformally invariant sigma models in D = 2n dimensions with target non-compact SO(2n, 1) groups are reviewed. Despite the non-compact nature of the SO(2n, 1) , the classical action and Hamiltonian are positive definite. Instanton field configurations are found to correspond geometrically to conformal "stereographic" mappings of R 2n into the Euclidean signature AdS 2n spaces. The relation between Self Dual branes and Chern-Simons branes , High Dimensional Knots , follows. A detailed discussion on W ∞ symmetry is given and we outline the Vasiliev procedure to construct an action involving higher spin massless fields in AdS 4 . This AdS 4 spacetime higher spin theory should have a one-to-one correspondence to noncritical W ∞ strings propagating on AdS 4 × S 7 .

Static potential from spontaneous breaking of scale symmetry

“…As was explained in [7], the scale invariant model under consideration introduces, in addition to the standard gauge fields also maximal rank gauge field strengths of four indices in four dimensions, F µναβ = ∂ [µ A ναβ] where A ναβ is a three index potential. The integration of the equations of motion of the A ναβ field introduces a constant of integration M which breaks the scale invariance [8]. More specifically, the linear term in the Cornell potential arises from the constant of integration M. Obviously, when M = 0 the equations of motion reduce to those of the standard gauge field theory.…”

“…where A ναβ is a three index potential. The integration of the equations of motion of the A ναβ field introduces a constant of integration M which breaks the scale invariance [8]. More specifically, the linear term in the Cornell potential arises from the constant of integration M. Obviously, when M = 0 the equations of motion reduce to those of the standard gauge field theory.…”