A new AdS/CFT correspondence

Abstract

We consider a geometric zero-radius limit for strings on $AdS_5\times S^5$, where the anti-de Sitter hyperboloid becomes the projective lightcone. In this limit the fifth dimension becomes nondynamical, yielding a different "holographic" interpretation than the usual "bulk to boundary" one. When quantized on the random lattice, the fifth coordinate acts as a new kind of Schwinger parameter, producing Feynman rules with normal propagators at the tree level: For example, in the bosonic case ordinary massless $\phi^4$ theory is obtained. In the superstring case we obtain new, manifestly ${\cal N}=4$ supersymmetric rules for ${\cal N}=4$ super Yang-Mills. These gluons are also different from those of the usual AdS/CFT correspondence: They are the "partons" that make up the usual "hadrons" of the open and closed strings in the familiar QCD string picture. Thus, their coupling $g_{YM}$ and rank $N$ of the "color" gauge group are different from those of the "flavor" gauge group of the open string. As a result we obtain different perturbation expansions in radius, coupling, and 1/N.