Sharpening the Distance Conjecture in diverse dimensions

The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory quantum gravity must be accompanied by tower light particles whose masses scale exponentially with proper distance $\Vert\phi\Vert$ as $m \sim \exp(- \lambda \Vert\phi\Vert)$, where $\lambda$ is order-one Planck units. While evidence for this conjecture formidable, there at present no consensus on which values are allowed. In paper, we propose sharp lower bound lightest given $d$ dimensions: $\lambda \geq 1/\sqrt{d-2}$. support proposal, show (1) it exactly preserved under dimensional reduction, (2) saturated many examples string/M-theory compactifications, including maximal supergravity $d= \text{4 - 10}$ dimensions, and (3) minimal assuming appropriate versions Weak Gravity Conjecture. We argue towers < 1/\sqrt{d-2}$ discussed previously literature always even lighter 1/\sqrt{d-2}$, thereby satisfying our proposed bound. discuss connections implications Emergent String Conjecture, Scalar Repulsive Force large-field inflation, potentials gravity. particular, if applies beyond massless spaces to fields potentials, then accelerated cosmological expansion cannot occur asymptotic regimes