Abstract
We argue that in theories of quantum gravity with discrete gauge symmetries, e.g. Zk , the gauge couplings of U(1) gauge symmetries become weak in the limit of large k, as g → k−α with α a positive order 1 coefficient. The conjecture is based on black hole arguments combined with the Weak Gravity Conjecture (or the BPS bound in the supersymmetric setup), and the species bound. We provide explicit examples based on type IIB on AdS5×S5/Zk orbifolds, and M-theory on AdS4×S7/Zk ABJM orbifolds (and their type IIA reductions). We study AdS4 vacua of type IIA on CY orientifold compactifications, and show that the parametric scale separation in certain infinite families is controlled by a discrete Zk symmetry for domain walls. We accordingly propose a refined version of the strong AdS Distance Conjecture, including a parametric dependence on the order of the discrete symmetry for 3-forms.
Highlights
Some results, see [9,10,11], and [12]), and mostly focus on the constrain that global discrete symmetries, just like global continuous symmetries, are forbidden in quantum gravity
We argue that in theories of quantum gravity with discrete gauge symmetries, e.g. Zk, the gauge couplings of U(1) gauge symmetries become weak in the limit of large k, as g → k−α with α a positive order 1 coefficient
We study AdS4 vacua of type IIA on CY orientifold compactifications, and show that the parametric scale separation in certain infinite families is controlled by a discrete Zk symmetry for domain walls
Summary
The fact that the WGC particles, whose defining feature has to do with the U(1) gauge symmetry, know about the Zk symmetry implies that there are cross constraints among the U(1) and the Zk symmetry. The particles that extremal black holes use to peel off their Zk charge are WGC particles, obey m ∼ g q Mp. We obtain that the gauge coupling of the U(1) must depend on k and should become weak fast enough in the large k limit, as g ∼ k−α. We obtain that the gauge coupling of the U(1) must depend on k and should become weak fast enough in the large k limit, as g ∼ k−α We propose this to be a general swampland constraint, as follows: Zk weak coupling conjecture. In a quantum gravity theory with a discrete Zk gauge symmetry and a U(1) gauge symmetry with coupling g, the gauge coupling scales as g ∼ k−α for large k, with α a positive order 1 coefficient.
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