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Discrete symmetries, weak coupling conjecture and scale separation in AdS vacua. (English) Zbl 1437.83035

Summary: We argue that in theories of quantum gravity with discrete gauge symmetries, e.g. \(\mathbb{Z}_k\), the gauge couplings of \(\mathrm{U}(1)\) gauge symmetries become weak in the limit of large \(k\), as \(g \rightarrow k^{-\alpha}\) with \(\alpha\) 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 \(\mathrm{AdS}_5 \times \mathbb{S}^5/\mathbb{Z}_k\) orbifolds, and M-theory on \(\mathrm{AdS}_4 \times \mathbb{S}^7/\mathbb{Z}_k\) ABJM orbifolds (and their type IIA reductions). We study \(\mathrm{AdS}_4\) vacua of type IIA on CY orientifold compactifications, and show that the parametric scale separation in certain infinite families is controlled by a discrete \(\mathbb{Z}_k\) 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.

MSC:

83C45 Quantization of the gravitational field
81T60 Supersymmetric field theories in quantum mechanics
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