# AdS and the Swampland

## TL;DR

This paper explores the connection between anti-de Sitter space and the Swampland, proposing that the flat limit involves an infinite tower of light states and relating this to broader Swampland conjectures and the behavior of de Sitter space.

## Contribution

It introduces a new conjecture linking the near-flat limit of AdS to the Swampland, with a power-law mass tower, and extends the distance conjecture to AdS radius variations.

## Key findings

- The near-flat limit of pure AdS is in the Swampland due to an infinite tower of light states.
- The mass of the light tower scales as a power-law with the cosmological constant, with a specific exponent for supersymmetric cases.
- The distance to the $\\Lambda \rightarrow 0$ limit in AdS is infinite, implying a light tower of states and connecting to the Swampland and de Sitter conjectures.

## 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 $\Lambda \rightarrow 0$ limit of AdS is infinite, leading to the light tower of states. We also discuss implications of the conjecture for de Sitter space.