Holography and Compactification

Abstract

Following a recent suggestion by Randall and Sundrum, we consider string compactification scenarios in which a compact slice of AdS-space arises as a subspace of the compactification manifold. A specific example is provided by the type II orientifold equivalent to type I theory on (orbifolds of) $T^6$, upon taking into account the gravitational backreaction of the D3-branes localized inside the $T^6$. The conformal factor of the four-dimensional metric depends exponentially on one of the compact directions, which, via the holographic correspondence, becomes identified with the renormalization group scale in the uncompactified world. This set-up can be viewed as a generalization of the AdS/CFT correspondence to boundary theories that include gravitational dynamics. A striking consequence is that, in this scenario, the fundamental Planck size string and the large N QCD string appear as (two different wavefunctions of) one and the same object.