We study the charge-to-mass ratios of BPS states in four-dimensional $$ \mathcal{N} $$ N = 2 supergravities arising from Calabi-Yau threefold compactifications of Type IIB string theory. We present a formula for the asymptotic charge-to-mass ratio valid for all limits in complex structure moduli space. This is achieved by using the sl(2)-structure that emerges in any such limit as described by asymptotic Hodge theory. The asymptotic charge-to-mass formula applies for sl(2)-elementary states that couple to the graviphoton asymptotically. Using this formula, we determine the radii of the ellipsoid that forms the extremality region of electric BPS black holes, which provides us with a general asymptotic bound on the charge-to-mass ratio for these theories. Finally, we comment on how these bounds for the Weak Gravity Conjecture relate to their counterparts in the asymptotic de Sitter Conjecture and Swampland Distance Conjecture.

We study a class of eight-supercharge little string theories (LSTs) on the world-volume of N M5-branes with transverse space S 1 × (C 2 /Z M ). These M-brane configurations compactified on a circle are dual to M D5-branes intersecting N NS5-branes on T 2 × R 7,1 as well as to F-theory compactified on a toric Calabi-Yau threefold X N,M . We argue that the Kähler cone of X N,M admits three regions associated with weakly coupled quiver gauge theories of gauge groups [U (N )] M , [U (M )] N and [U ( N M k )] k where k = gcd(N, M ). These provide low-energy descriptions of different LSTs. The duality between the first two gauge theories is well known and is a consequence of the S-duality between D5-and NS5-branes or the T-duality of the LSTs. The triality involving the third gauge theory is new and we demonstrate it using several examples. We also discuss implications of this triality for the W-algebras associated with the Alday-Gaiotto-Tachikawa dual theories.