Holography vs. Scale Separation

TL;DR

The work demonstrates a fundamental tension between holography and parametric AdS scale separation in string theory by deriving the Asymptotic No-Scale-Separation Condition (ANSS) that a brane-worldvolume CFT must satisfy to decouple from bulk gravity. By reconstructing black branes from AdS data and employing a double Wick rotation to map to FRW cosmologies, the authors show that violating ANSS prevents a decoupling limit, thereby ruling out the existence of a holographic brane dual for such scale-separated AdS vacua (e.g., DGKT). They extend the analysis to KKLT and other Ricci-flat scenarios, arguing that their CFT duals cannot arise from decoupled brane dynamics. In addition, they apply the framework to dS/CFT, arguing that no Euclidean CFT dual can be realized on a brane, underscoring a broader obstruction for holographic descriptions of de Sitter space in string theory. Overall, the results constrain the landscape of UV-complete AdS constructions and suggest that scale-separated AdS vacua lack a consistent holographic embedding in string theory, with profound implications for cosmology and the string landscape.

Abstract

In this work, we point out a contradiction between holography and scale-separated AdS (i.e. parametrically large mass gap) in string theory, making the standard assumption that the holographic CFT describes the IR degrees of freedom on a brane that decouple from gravity. We show that the CFT can only decouple from gravity if the scalar potential in the dual AdS satisfies a certain criterion. Namely, there must exist a scalar field trajectory that follows the gradient of the scalar potential to the asymptotic region of the scalar field space in which limit $\partial_φ\ln(V)\partial_φ\ln(Λ_s)\leq2/(d-2)$, where $Λ_s$ is the quantum gravity cut-off. This condition, which generically implies lack of scale-separation, is satisfied in the standard examples of AdS/CFT. However, proposed attempts at achieving scale separation, such as DGKT, employ scalar potentials that violate this condition. We therefore conclude that the CFT duals of DGKT vacua cannot exist in string theory. Barring fine-tuning, our conclusions apply to other Ricci-flat flux compactifications including the KKLT scenario which relies on scale separation to obtain a metastable de Sitter uplift.

Figures (8)

• Figure 1: The above figure illustrates the massless moduli space of an AdS vacuum, or equivalently, in the CFT language, the conformal manifold of its dual CFT. Except for a finite region where the mass scale $|\Lambda_{\rm AdS}|^{1/2}$ associated with the AdS curvature remains below the quantum gravity cutoff $\Lambda_s$ the AdS description becomes strongly coupled, while the CFT description provides a weakly coupled framework. The quantum gravity cutoff is set by the string scale or the higher-dimensional Planck scale.
• Figure 2: Extremal black brane in an asymptotically AdS$_D$ spacetime.
• Figure 3: Modes with local energy $E$ in the throat at $\rho = \rho_i$ experience a gravitational redshift as they propagate to the asymptotic region $\rho_o \gg L$.
• Figure 4: Reconstruction of the brane (in red) from a scalar potential with a minimum at $\phi_0$ and $V \to 0$ as $\phi \to \infty$.
• Figure 5: The Double Wick Rotation of the black brane solution is an FRW solution which in the past infinity asymptotes to de Sitter space and in the future infinity is a scalar field cosmology driven by an exponential positive scalar potential.