Sharpening the Distance Conjecture in diverse dimensions

Abstract

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.

(Quasi-) de Sitter solutions across dimensions and the TCC bound

“…Another important proposal in the literature is that of [34,59], revisited recently in [15,60]. As for the TCC, it is meant to hold in the asymptotics of field space.…”

“…In [60], a different interpretation of the above was considered by introducing a lower bound λ min = 1 √ d−2 that would correspond to the minimal rate of the lightest tower. In other words, even though it is possible to have a tower decaying at a rate , [60] suggests that one can then find a lighter tower, thus decaying with a higher rate, which has to be bigger than 1 √ d−2 . This interpretation allows to verify a relation (5.6) with α = 1 2 , considering the bound (5.3) for c that we discussed above.…”

Constraints on early dark energy from the axion weak gravity conjecture

“…Furthermore, because our arguments relied on rather generic scaling behavior of Kaluza-Klein modes and wound strings, we expect that they will carry over to heterotic string heterotic string theories on T n , and thus to M-theory/Type IIA string theory on K3, by duality. We will explore these scenarios further in a forthcoming work [13].…”

Dynamical Cobordism Conjecture: Solutions for End-of-the-World Branes

“…where λ SDC is an O(1) constant and D is the distance in moduli space. Recently, in [32] the authors made a strong effort to sharpen the conjecture and proposed constraints on λ SDC . In the context of our analysis the upper bound…”

“…The previous analysis reveals the appearance of a lower bound δ ≥ 2 (D − 1)/(D − 2) for the critical exponent in the scaling behavior of the distance and the curvature close to the wall. We will argue for a connection to the (sharpened) Swampland Distance Conjecture [32] and the (anti-) de Sitter Distance Conjecture [33].…”