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 non-trivial condition of the weak gravity conjecture. As concrete examples, we consider $U(1)^{k}$ gauge theories with a discrete symmetry associated with cyclic permutations between the gauge groups, and identify anomaly-free $U(1)$ 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 $U(1)$ 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.
Highlights
Swampland conjectures attract much attention recently in various aspects [1,2,3,4,5,6,7]
If the weak gravity conjecture (WGC) is correct and the ratio of m=MPl remains fixed in the large k limit. This upper bound on k is similar to the species bound [27], but k is not the number of species but the number of Uð1Þ gauge groups in our
To check strong scalar weak gravity conjecture (SWGC) [11] for φ is an interesting issue, but this is left for future work and we focus on the SWGC for fermions with nontrivial anomaly-free gauge charges
Summary
Swampland conjectures attract much attention recently in various aspects [1,2,3,4,5,6,7]. The linear combinations are determined by the Stückelberg couplings among the gauge bosons and would-be Nambu-Goldstone bosons (or axions) associated with the symmetry breaking This is applicable to anomaly-free gauge theories and to consistent theories possessing anomalous Uð1Þ gauge groups. Instead of concrete string models, in this paper we will consider quiver gauge theories with Uð1Þk gauge groups and focus on the anomaly-free gauge groups and the (S)WGC in a bottom-up approach, supposing that the remaining anomalies are canceled and the anomalous gauge bosons get massive. In order to check anomaly-free Uð1Þ’s systematically and study concretely the (S)WGC constraints on the gauge couplings, we restrict ourselves to several types of models controlled by discrete symmetries. We will discuss the above arguments with the tree level parameters
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