A bstract We give evidence that fully supersymmetric Anti-de Sitter vacua of extended supergravity with a residual gauge group containing an abelian factor cannot be scale separated as consequence the weak gravity conjecture. prove this for N = 2 and 8 we explain how our argument applies also to partially broken, but supersymmetry. finally discuss possible loopholes especially certain 1 models ...

For an odd integer r>0 and n>r, we introduce a notion of weakly r-separated collections subsets [n]={1,2,…,n}. When r=1, this corresponds to the concept weak separation introduced by Leclerc Zelevinsky. In paper, extending results due Leclerc-Zelevinsky, develop geometric approach establish number nice combinatorial properties maximal (such as exact upper bound on size collections, mutations ru...

We continue the work of [14, 3, 1, 19, 16, 4, 12, 11, 20] investigating the strength of set existence axioms needed for separable Banach space theory. We show that the separation theorem for open convex sets is equivalent to WKL0 over RCA0. We show that the separation theorem for separably closed convex sets is equivalent to ACA0 over RCA0. Our strategy for proving these geometrical Hahn–Banach...

A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. The aim of this paper is to present some interesting weak metrics and to study some of their properties. In particular, we introduce a weak metric, called the Apollonian weak metric, on any subset of a Euclidean space which is either bounded or whose boundary is unbounded. W...