AdS and the Swampland

Abstract

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