Expanding the Weak Gravity Conjecture in AdS Space

TL;DR

This work extends the Weak Gravity Conjecture to anti–de Sitter spaces with moduli by formulating a near-horizon repulsive-force criterion for black hole decay via the Schwinger effect. It shows that, before moduli stabilization, the AdS WGC bound is background-independent and matches flat-space expectations, while after stabilization, a non-singular horizon yields a corrected AdS bound that depends on the horizon size and dilaton value. The analysis covers RN and EMD black holes in both Minkowski and AdS, deriving explicit bounds such as $rac{M_{Pl}^{D-2} g^2 q^2}{m^2}\ge rac{D-3}{D-2}$ in flat space and its AdS counterparts with horizon-dependent corrections; it also argues for a tower WGC in AdS under dimensional reduction. The results suggest the AdS WGC remains compatible with tower/distance conjectures and motivate tests in AdS string compactifications and AdS$_m imes S^n$ backgrounds.

Abstract

In this work, we investigate the extension of our recent proposal for the Weak Gravity Conjecture (WGC) in AdS space to more general effective field theories. We first extend the conjecture to set-ups where moduli are present and we demand that a particle, produced during the decay of an extremal black hole via the Schwinger effect, is repelled close to the horizon of the black hole. We interpret this condition as the universal criterion imposed by the WGC for any background. Interestingly, the constraint imposed by the WGC on the particle spectrum, before the stabilization of the moduli, is independent of the background, resulting in the same bound both in Minkowski and in AdS space. For the case of AdS space, after the stabilization of the moduli, the WGC in AdS space is reproduced due to the formation of a non-singular horizon of the extremal black hole. In that case, the particle spectrum must satisfy the stronger of the two WGC conditions obtained before and after moduli stabilization. Finally, we use these results to argue that a similar version of the tower WGC should also apply to an AdS background.

Figures (1)

• Figure 1: The parameter space for dilaton-stabilized black hole solutions. Horizontal axis represents the dilaton mass $\mu$ and the vertical axis represents the allowed black hole size $r_h$ that the dilaton can be stabilized, all in units of the AdS length $\ell_\text{\tiny AdS,\,D}=1$. There is a minimum dilaton mass $\mu^2 \gtrsim|\Lambda_\text{\tiny AdS,\,D}|$ requirement for the stabilization to happen. For any $\mu$, there is a minimum black hole size $r_\text{\tiny h,min.}$ below which the curvature scale dominates over the dilaton mass and the black hole becomes singular.