Implications of the weak gravity conjecture in anomalous quiver gauge theories

Abstract

We argue a smallness of gauge couplings in Abelian quiver gauge theories, taking the anomaly cancellation condition into account. In theories of our interest there exist chiral fermions leading to chiral gauge anomalies, and an anomaly-free gauge coupling tends to be small, and hence can give a nontrivial condition of the weak gravity conjecture. As concrete examples, we consider Uð1Þ k gauge theories with a discrete symmetry associated with cyclic permutations between the gauge groups, and identify anomalyfree Uð1Þ gauge symmetries and the corresponding gauge couplings. Owing to this discrete symmetry, we can systematically study the models and we find that the models would be examples of the weak coupling conjecture. It is conjectured that a certain class of chiral gauge theories with too many Uð1Þ symmetries may be in the swampland. We also numerically study constraints on the couplings from the scalar weak gravity conjecture in a concrete model. These constraints may have a phenomenological implication to model building of a chiral hidden sector as well as the visible sector.