On the large N limit, W_\infty Strings, Star products, AdS/CFT Duality, Nonlinear Sigma Models on AdS spaces and Chern-Simons p-branes

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 $AdS/CFT$ 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 $Ad{S}_{2n}$ spaces. The relation between Self Dual branes and Chern-Simons branes, High Dimensional Knots, follows. A detailed discussion on $W_{\infty }$ symmetry is given and we outline the Vasiliev procedure to construct an action involving higher spin massless fields in $Ad{S}_4$. This $Ad{S}_4$ spacetime higher spin theory should have a one-to-one correspondence to noncritical $W_{\infty }$ strings propagating on $Ad{S}_4\times S^7$.

43 pages, Tex file

References in corpus (5)

• The Holographic Renormalization Group
• Faddeev-Niemi Conjecture and Effective Action of QCD
• Higher-Derivative Gravity and the AdS/CFT Correspondence
• Nambu-Goto Strings from SU(N) Born-Infeld model
• W Algebras from AdS/CFT Correspondence

Cited by in corpus (1)

• Static potential from spontaneous breaking of scale symmetry