Holographic Constraints on the String Landscape

TL;DR

This work develops holographic consistency conditions for scalar potentials in the string landscape by analyzing infinite-distance limits in moduli space and their brane/worldvolume duals. It introduces four constraints (C1–C4) linking TCC, ANSS, brane decoupling, and a steepness bound to the asymptotic behavior of $V$ and the species scale $\Lambda_s$, deriving concrete exclusions for positive and negative potentials. The analysis rules out long plateau cosmologies, imposes exponential fall-offs with $V(\phi) \sim e^{-\lambda\phi}$ where $\lambda \ge \sqrt{2}$, and disfavors AdS constructions like DGKT and KKLT under the assumption of a brane-based holographic dual, while highlighting subtle multi-field possibilities. The results provide a global, boundary-informed diagnostic that connects interior potential shapes to asymptotic moduli-space structure, strengthening swampland constraints and informing which holographic duals are viable.

Abstract

We show that holography imposes strong and general constraints on scalar field potentials in the string landscape, determined by the asymptotic structure of the underlying spacetime. Applying these holographic consistency conditions, we identify broad classes of scalar potentials that are incompatible with a well-defined dual description. These include potentials with extended plateaus, excessively steep or shallow asymptotics, certain zero crossings, and specific alignments of stable AdS minima in moduli space. In particular, making the standard assumption that the CFT dual to a stable AdS vacuum must be realized as a worldvolume theory of a brane in string theory, we show that the brane selects an infinite-distance limit in moduli space where parametric scale separation is forbidden. Furthermore, the steepness and positivity of the potential are restricted in that infinite distance direction. We also find that requiring the validity of the effective theory in the future vacuum, a natural holographic criterion, automatically enforces the Trans-Planckian Censorship Conjecture (TCC) for classical cosmological solutions with positive potentials. Taken together, these constraints exclude the leading proposals to realize scale-separated AdS vacua and metastable de Sitter vacua in the string theory landscape such as DGKT and KKLT.

Figures (3)

• Figure 1: $V_{\rm DGKT}(\phi) =10^4 e^{-\sqrt{\frac{{26}}{{3}}}\phi} - e^{-3\sqrt{\frac{{6}}{{13}}}\phi}$. At large $\phi$, the potential violates the Asymptotic No–Scale–Separation condition, and is therefore excluded by holography.
• Figure 2: Example of a ruled–out potential which crosses zero and approaches zero from the positive side, violating the Asymptotic No–Scale–Separation condition.
• Figure 3: Illustration of a scalar potential $V(\phi)$ (top) and its Euclidean counterpart $V_E(\phi)=-V(\phi)$ (bottom). The two minima $\phi_1$ and $\phi_2$ correspond to AdS vacua in the Lorentzian potential, which appear as maxima in the Euclidean potential $V_E$. This correspondence clarifies the relation between CDL instantons and black--brane domain walls.