Abstract
We analyze the charge-to-mass structure of BPS states in general infinite-distance limits of mathcal{N} = 2 compactifications of Type IIB string theory on Calabi-Yau three-folds, and use the results to sharpen the formulation of the Swampland Conjectures in the presence of multiple gauge and scalar fields. We show that the BPS bound coincides with the black hole extremality bound in these infinite distance limits, and that the charge-to-mass vectors of the BPS states lie on degenerate ellipsoids with only two non-degenerate directions, regardless of the number of moduli or gauge fields. We provide the numerical value of the principal radii of the ellipsoid in terms of the classification of the singularity that is being approached. We use these findings to inform the Swampland Distance Conjecture, which states that a tower of states becomes exponentially light along geodesic trajectories towards infinite field distance. We place general bounds on the mass decay rate λ of this tower in terms of the black hole extremality bound, which in our setup implies lambda ge 1/sqrt{6} . We expect this framework to persist beyond mathcal{N} = 2 as long as a gauge coupling becomes small in the infinite field distance limit.
Highlights
Whether the exponential factor of the Swampland Distance Conjecture (SDC) can be fully determined by the extremality bound for black holes in the asymptotic limits depends on whether the Weak Gravity Conjecture (WGC) in the presence of scalar fields is equivalent to a repulsive force condition
In [16] it was argued that the WGC and the Repuslive Force Conjecture (RFC) coincide at the weak coupling limits, and this is the line of thought we have developed in this paper
We have analyzed the structure of BPS charge-to-mass ratios in the asymptotic limits of compactifications of Type IIB string theory on Calabi-Yau threefolds and used the results to sharpen the Swampland Conjectures in the presence of multiple gauge and scalar fields
Summary
We will test and sharpen the WGC and SDC by studying the properties of BPS states and the interrelations that appear among them. These individual αi will still be associated to the scalar contribution to the extremality bound of some particular black holes that satisfy (2.7). We will ignore the possible presence of these walls and just discuss the conal strucuture of charges that can in principle support BPS states, leaving a more detailed study to section 4
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