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Register a new userDiscrete Symmetries, Weak Coupling Conjecture and Scale Separation in AdS Vacua
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We argue that in theories of quantum gravity with discrete gauge symmetries, e.g. $textbf{Z}_k$, the gauge couplings of U$(1)$ gauge symmetries become weak in the limit of large $k$, as $gto k^{-alpha}$ 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 AdS$_5times textbf{S}^5/textbf{Z}_k$ orbifolds, and M-theory on AdS$_4timestextbf{S}^7/textbf{Z}_k$ ABJM orbifolds (and their type IIA reductions). We study 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 $textbf{Z}_k$ 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.
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In theories with discrete Abelian gauge groups, requiring that black holes be able to lose their charge as they evaporate leads to an upper bound on the product of a charged particles mass and the cutoff scale above which the effective description of the theory breaks down. This suggests that a non-trivial version of the Weak Gravity Conjecture (WGC) may also apply to gauge symmetries that are discrete, despite there being no associated massless field, therefore pushing the conjecture beyond the slogan that `gravity is the weakest force. Here, we take a step towards making this expectation more precise by studying $mathbb{Z}_N$ and $mathbb{Z}_2^N$ gauge symmetries realised via theories of spontaneous symmetry breaking. We show that applying the WGC to a dual description of an Abelian Higgs model leads to constraints that allow us to saturate but not violate existing bounds on discrete symmetries based on black hole arguments. In this setting, considering the effect of discrete hair on black holes naturally identifies the cutoff of the effective theory with the scale of spontaneous symmetry breaking, and provides a mechanism through which discrete hair can be lost without modifying the gravitational sector. We explore the possible implications of these arguments for understanding the smallness of the weak scale compared to $M_{Pl}$.
We construct AdS$_4$ flux vacua of type IIA string theory in the supergravity (large volume, small $g_s$) regime, including the backreaction of O6-planes. Our solutions are the localiz
We revisit various aspects of AdS$_4$ flux vacua with scale separation in type II supergravity and M-theory. We show that massless IIA allows both weakly and strongly coupled solutions for which the classical orientifold backreaction can be tuned small. This is explicitly verified by computing the backreaction at leading order in perturbation theory. We give evidence that the strongly coupled solutions can be lifted to scale-separated and sourceless (but classically singular) geometries in 11D supergravity.
McNamara and Vafa conjectured that any pair of consistent quantum gravity theories can be connected by a domain wall. We test the conjecture in the context of the AdS/CFT correspondence. There are topological constraints on existence of an interface between the corresponding conformal field theories. We discuss how to construct domain walls in AdS predicted by the conjecture when the corresponding conformal interfaces are prohibited by topological obstructions.
The Schwarzschild, Schwarzschild-AdS, and Schwarzschild-de Sitter solutions all admit freely acting discrete involutions which commute with the continuous symmetries of the spacetimes. Intuitively, these involutions correspond to the antipodal map of the corresponding spacetimes. In analogy with the ordinary de Sitter example, this allows us to construct new vacua by performing a Mottola-Allen transform on the modes associated with the Hartle-Hawking, or Euclidean, vacuum. These vacua are the `alpha-vacua for these black holes. The causal structure of a typical black hole may ameliorate certain difficulties which are encountered in the case of de Sitter alpha-vacua. For Schwarzschild-AdS black holes, a Bogoliubov transformation which mixes operators of the two boundary CFTs provides a construction of the dual CFT alpha-states. Finally, we analyze the thermal properties of these vacua.
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