Holography and Compactification
Herman Verlinde
TL;DR
Verlinde extends AdS/CFT by embedding a compact AdS slice into a string compactification and promoting the holographic RG scale to a physical extra dimension, thereby incorporating gravity on the boundary. In a concrete setup with type I orientifolds on $T^6$ and D3-branes, an $AdS_5\times S^5$ throat emerges and can be glued into the compactification, yielding a normalizable 4D graviton and a warped relation between 10D and 4D scales. The framework links Planck-scale strings to large-N gauge-string excitations as two wavefunctions of the same underlying object and suggests new routes to phenomenology, hierarchy issues, and cosmology within holographic compactifications. Practical realization requires navigating tadpole constraints, backreaction, and finite-$N$ effects, but the approach broadens the scope of AdS/CFT to gravity-inclusive boundary theories with potential low-energy implications.
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.