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A bstract The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field distance ‖ ϕ ‖ as m ~ exp(− λ ‖ ϕ ‖), where λ is order-one in Planck units. While the evidence for this conjecture is formidable, there is at present no consensus on which values of λ are allowed. In this paper, we propose a sharp lower bound for the lightest tower in a given infinite-distance limit in d dimensions: λ ≥ $$ 1/\sqrt{d-2} $$ 1 / d − 2 . In support of this proposal, we show that (1) it is exactly preserved under dimensional reduction, (2) it is saturated in many examples of string/M-theory compactifications, including maximal supergravity in d = 4 – 10 dimensions, and (3) it is saturated in many examples of minimal supergravity in d = 4 – 10 dimensions, assuming appropriate versions of the Weak Gravity Conjecture. We argue that towers with λ < $$ 1/\sqrt{d-2} $$ 1 / d − 2 discussed previously in the literature are always accompanied by even lighter towers with λ ≥ $$ 1/\sqrt{d-2} $$ 1 / d − 2 , thereby satisfying our proposed bound. We discuss connections with and implications for the Emergent String Conjecture, the Scalar Weak Gravity Conjecture, the Repulsive Force Conjecture, large-field inflation, and scalar field potentials in quantum gravity. In particular, we argue that if our proposed bound applies beyond massless moduli spaces to scalar fields with potentials, then accelerated cosmological expansion cannot occur in asymptotic regimes of scalar field space in quantum gravity.
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This content will become publicly available on September 18, 2026
A Distance Conjecture for branes
We use branes to generalize the Distance Conjecture. We conjecture that in any infinite-distance limit in the moduli space of a d-dimensional quantum gravity theory, among the set of particle towers and fundamental branes with at most pmax spacetime dimensions (where pmax is an integer between 1 and d-2), at least one has mass/tension decreasing exponentially T ~ exp(–α ∆) with the moduli space distance ∆ at a rate of at least α ≥ 1/sqrt(d-pmax-1). Since pmax can vary, this represents multiple conditions, where the Sharpened Distance Conjecture is the pmax = 1 case. This conjecture is a necessary condition imposed on higher-dimensional theories in order for the Sharpened Distance Conjecture to hold in lower-dimensional theories. We test our conjecture in theories with maximal and half-maximal supersymmetry in diverse dimensions, finding that it is satisfied and often saturated. In some cases where it is saturated — most notably, heterotic string theory in 10 dimensions — we argue that novel, low-tension non-supersymmetric branes must exist. We also identify patterns relating the rates at which various brane tensions vary in infinite-distance limits and relate these tensions to the species scale.
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- PAR ID:
- 10646705
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2025
- Issue:
- 9
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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