The AdS distance conjecture

Consider a one-parameter family of $D$-dimensional Anti-de Sitter metrics $g_{\mu\nu}(\Lambda)$ arising as quantum-gravity low-energy effective theories, labelled by their cosmological constant $\Lambda$. Let $\mathbf{M}_\Lambda\sim\mathbb{R}_{-}$ be the corresponding moduli space. AdS distance conjecture. There must exist an infinite tower of fields with a moduli-dependent mass threshold $m:\mathbf{M}_\Lambda\to\mathbb{R}$ such that, in the flat-space limit $\Lambda\to0$,

$$m\sim|\Lambda|^\alpha,$$

where, in Planck units, $\alpha$ is positive and of order one.

The conjecture applies the distance-conjecture idea to the cosmological-constant direction in AdS moduli space. Kaluza–Klein towers in explicit compactifications motivate the power-law scaling, but the general conjecture remains open.