Holographic Constraints on the String Landscape (2511.15784v1)

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.

• The paper establishes holographic criteria that constrain scalar field potentials in string effective theories, rigorously excluding certain scale-separated AdS and dS vacua.
• It leverages AdS/CFT duality and the emergence of light-state towers to derive conditions on potential steepness and asymptotic moduli behavior.
• The findings have substantial implications for inflation, moduli stabilization, and the viability of constructions like DGKT and KKLT.

Holographic Constraints on the String Landscape: A Technical Overview

Introduction

"Holographic Constraints on the String Landscape" (2511.15784) establishes general criteria, derived from holographic principles, for the admissibility of scalar field potentials within effective theories arising from string compactifications. The methodology leverages the connection between the asymptotic behavior of spacetime moduli and the existence of consistent holographic duals. The paper synthesizes bottom–up reasoning based on the boundary structure of AdS/CFT duality and the emergence of towers of light states at infinite-distance limits, yielding rigorous constraints relevant to both positive and negative scalar potentials. These criteria have direct implications for prominent landscape constructions such as DGKT and KKLT, excluding their scale-separated AdS and metastable dS vacua under natural holographic assumptions.

Holographic Consistency and Scalar Potentials

Four central conditions (C1–C4) are articulated:

• C1 (TCC for classical scalar cosmologies): Every expanding, spatially flat FRW cosmology with a scalar rolling to infinite distance (without tunneling) must obey the Trans-Planckian Censorship Conjecture (TCC). The validity of the effective theory in the future vacuum enforces this restriction on the size and nature of positive potentials.
• C2 (Asymptotic No-Scale-Separation, ANSS): For each stable AdS minimum, there exists an infinite-distance flow direction $\nabla V$ with $V \to 0^-$ such that $$\partial_\phi\ln V \cdot \partial_\phi\ln\Lambda_s \leq 2/(d-2)$$, where $\Lambda_s$ denotes the quantum gravity cutoff, typically set by the species scale. This precludes parametric scale separation.
• C3 (Existence of a brane): There must be a warped, stationary solution—interpreted as a worldvolume brane—where the scalar interpolates between the AdS critical point and the infinite-distance asymptotic regime, supporting the emergence of a nontrivial holographic dual.
• C4 (Bound on Potential Steepness): In the infinite-distance limit of $V\to0^-$, the asymptotic slope satisfies $|\nabla V / V| \leq 2\sqrt{(d-1)/(d-2)}$, excluding excessively steep potentials from admitting a consistent dual description.

Collectively, these constraints robustly characterize the allowed shape and scale of scalar potentials independently of the microscopic string realization.

Exclusion of Scale-Separated AdS and dS Landscapes

Application of the above constraints systematically excludes key classes of potentials:

• Steepness in Positive Potentials: For single-field models in $d=4$ dimensions, the asymptotic falloff of positive potentials must exceed $\lambda \geq \sqrt{2}$ in the exponential decay $V\sim e^{-\lambda\phi}$, precluding power-law inflation and violating slow-roll plateaus extending to infinite field distance. This enforces the original TCC bounds and prohibits inflationary models with long flat plateaus unless they terminate in metastable dS minima.
• Plateaus and the TCC: Extended plateaus that do not terminate and allow trajectories to run to infinity are ruled out. For example, if a trajectory enables $N$ e-folds, TCC enforces $N<\ln(M_\text{Pl}^2/V_0^{1/2})$, sharply bounding possible cosmological histories.
• Negative Potentials & Scale Separation: The leading proposals for scale-separated AdS vacua, such as DGKT (DeWolfe-Giryavets-Kachru-Taylor) and KKLT (Kachru-Kallosh-Linde-Trivedi), are shown to be incompatible with holographic decoupling. DGKT's species scale and potential decay violate ANSS, while KKLT's nonperturbative double-exponential decay leads to a steepness parameter diverging in the infinite-distance limit, precluding the necessary black-brane interpolating solution.
• Zero crossings: Scalar potentials with asymptotics approaching zero from the positive side (in a landscape with a stable AdS minimum) are forbidden, as a black-brane solution requires the potential to remain negative.
• Multiplicity of AdS Minima: In one-dimensional moduli spaces, the existence of multiple stable AdS vacua violates the requirement for a domain-wall solution interpolating from a minimum to infinity; the AdS minimum nearer the infinite-distance region stably obstructs the flow, rendering such landscapes inconsistent with holography.

Multi-Field Generalizations

Generalization to multi-moduli landscapes refines these constraints:

• Each stable AdS vacuum requires a distinct black-brane solution aligned with a particular direction in moduli space. Potentials may admit multiple AdS minima provided they are not aligned along the same flow; in intricate moduli spaces, such as M-theory compactified on squashed $S^7$, distinct moduli permit this multiplicity.
• For positive potentials, every classical path connecting interior plateaus to asymptotia must obey TCC, implying that the allowed landscape configurations are highly fine-tuned and exceptional.
• In the KKLT context, every infinite-distance direction is either dominated by perturbative (non-negative) contributions or nonperturbative (double-exponential, infinitely steep) potentials—both violate at least one of the required holographic inequalities, excluding their AdS vacua from possessing consistent CFT duals as brane worldvolume theories.

Implications and Outlook

These constraints significantly sharpen the swampland/landscape dichotomy:

• Theoretical Implications: The analysis provides global diagnostics that operate independently of local moduli space details or explicit string construction, allowing one to rigorously exclude vast classes of effective potentials from admitting a holographic dual. This elevates the role of boundary behavior in assessing consistency and dramatically narrows the space of viable low-energy string vacua.
• Practical Impact: Inflationary cosmology model-building and moduli stabilization schemes must address these constraints, eschewing plateau-based inflation unless metastability structures are explicitly realized and ensuring that any AdS minimum admits a flow and species scale compatible with the derived bounds.
• Future Directions: The methodology may be extended to assess non-supersymmetric vacua, probe the interplay between black-brane singularities and holographic decoupling in higher-derivative regimes, and unify swampland constraints with explicit AdS/CFT dictionary refinements. The universality of the emerging tower of light states at moduli space infinity remains a promising vantage point for future global swampland conjectures.

Conclusion

"Holographic Constraints on the String Landscape" offers powerful, holographically motivated criteria for the admissibility of scalar field potentials in string effective theories. These constraints operate globally, tie the interior structure directly to asymptotic moduli dynamics, and categorically exclude leading constructions of scale-separated AdS and metastable dS vacua under conventional holographic assumptions. The approach sets a rigorous foundation for further delineation of the swampland and suggests promising pathways for near-term and longer-term theoretical progress in quantum gravity and string phenomenology.