AdS Distance Conjecture and Towers of Light States from Compact Dimensions

Prove the AdS distance conjecture by establishing that compactifications yielding anti‑de Sitter vacua necessarily produce towers of light states, implying that the extra compact dimensions are not extremely small and may populate the dark sector.

Background

The AdS distance conjecture predicts that approaching certain limits in moduli space leads to infinite towers of light states, constraining how extra dimensions manifest in low‑energy physics. The authors summarize its strongest‑form implication: compact dimensions cannot be arbitrarily small and must generate light towers potentially relevant for dark matter.

If verified, this conjecture would imply observable consequences at relatively accessible energy scales, influencing searches for new physics and shaping expectations about the spectrum of states in EFTs derived from string compactifications.