AdS and the Swampland

TL;DR

This work proposes the AdS Distance Conjecture (ADC), asserting that as the AdS cosmological constant $\Lambda$ approaches zero, an infinite tower of states becomes light with mass $m \sim |\Lambda|^{\alpha}$, where $\alpha = O(1)$ (often $\alpha=\tfrac{1}{2}$ in SUSY). It introduces a Generalized Distance Conjecture that assigns a field-space distance $\Delta$ to variations of all fields and shows that $m$ scales as $m \sim e^{-\alpha \Delta}$, providing a unifying framework for understanding how AdS radius changes couple to light towers. The paper connects these ideas to the refined de Sitter conjecture, discusses implications for de Sitter space via the Higuchi bound, and surveys string-theory vacua (KKLT, LVS, DGKT) in light of ADC, arguing that an infinite tower of light states appears as $|\Lambda| \to 0$ and that near-pure AdS cannot be isolated in quantum gravity. Overall, the work strengthens the view that AdS, Minkowski, and dS vacua occupy infinite-distance sectors of field space and supports swampland constraints against stable de Sitter realizations, with potential cosmological and dark-sector phenomenology stemming from light towers.

Abstract

We study aspects of anti-de Sitter space in the context of the Swampland. In particular, we conjecture that the near-flat limit of pure AdS belongs to the Swampland, as it is necessarily accompanied by an infinite tower of light states. The mass of the tower is power-law in the cosmological constant, with a power of $\frac{1}{2}$ for the supersymmetric case. We discuss relations between this behaviour and other Swampland conjectures such as the censorship of an unbounded number of massless fields, and the refined de Sitter conjecture. Moreover, we propose that changes to the AdS radius have an interpretation in terms of a generalised distance conjecture which associates a distance to variations of all fields. In this framework, we argue that the distance to the $Λ\rightarrow 0$ limit of AdS is infinite, leading to the light tower of states. We also discuss implications of the conjecture for de Sitter space.