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Register a new userA NUT Charge Weak Gravity Conjecture from Dimensional Reduction
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We analyze the constraints on four-derivative corrections to 5d Einstein-Maxwell theory from the black hole Weak Gravity Conjecture (WGC). We calculate the leading corrections to the extremal mass of asymptotically flat 5d charged solutions as well as 4d Kaluza-Klein compactifications. The WGC bounds from the latter, interpreted as 4d dyonic black holes, are found to be strictly stronger. As magnetic graviphoton charge lifts to a NUT-like charge in 5d, we argue that the logic of the WGC should apply to these topological charges as well and leads to new constraints on purely gravitational theories.
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The Weak Gravity Conjecture (WGC) was proposed to constrain Effective Field Theories (EFTs) with Abelian gauge symmetry coupled to gravity. In this article, I study the WGC from low energy observers perspective, and revisit the issue of to what extent the WGC actually constrains EFTs. For this purpose, for a given EFT, I introduce associated idealized low energy observers who only have access to the energy scale below the UV cut-off scale of the EFT. In the framework of EFT, there is a clear difference between the particles lighter than the UV cut-off scale and the particles which are heavier than the UV cut-off scale, as the lighter particles can be created below the UV cut-off scale while the heavier particles are not. This difference implies that the knowledge of the low energy observers on the stable heavy particles can be limited, as the availability of the stable heavy particles is determined by the environment prepared by some UV theory unknown to the low energy observers. The limitation of the knowledge of the low energy observers regarding the stable heavy particles whose mass is above the UV cut-off scale of the EFT leads to the limitation of the WGC for constraining EFTs. To illustrate these points in an example, I analyze a model proposed by Saraswat arXiv:1608.06951 which respects the WGC at high energy, but which may appear to violate the WGC for the low energy observers. Implications of the analysis to the bottom-up model buildings using EFTs are discussed.
The mild form of the Weak Gravity Conjecture states that quantum or higher-derivative corrections should decrease the mass of large extremal charged black holes at fixed charge. This allows extremal black holes to decay, unless protected by a symmetry (such as supersymmetry). We reformulate this conjecture as an integrated condition on the effective stress tensor capturing the effect of quantum or higher-derivative corrections. In addition to charged black holes, we also consider rotating BTZ black holes and show that this condition is satisfied as a consequence of the $c$-theorem, proving a spinning version of the Weak Gravity Conjecture. We also apply our results to a five-dimensional boosted black string with higher-derivative corrections. The boosted black string has a $text{BTZ}times S^2$ near-horizon geometry and, after Kaluza-Klein reduction, describes a four-dimensional charged black hole. Combining the spinning and charged Weak Gravity Conjecture we obtain positivity bounds on the five-dimensional Wilson coefficients that are stronger than those obtained from charged black holes alone.
We derive new positivity bounds for scattering amplitudes in theories with a massless graviton in the spectrum in four spacetime dimensions, of relevance for the weak gravity conjecture and modified gravity theories. The bounds imply that extremal black holes are self-repulsive, $M/|Q|<1$ in suitable units, and that they are unstable to decay to smaller extremal black holes, providing an S-matrix proof of the weak gravity conjecture. We also present other applications of our bounds to the effective field theory of axions, $P(X)$ theories, weakly broken galileons, and curved spacetimes.
It is widely believed and in part established that exact global symmetries are inconsistent with quantum gravity. One then expects that approximate global symmetries can be quantitatively constrained by quantum gravity or swampland arguments. We provide such a bound for an important class of global symmetries: Those arising from a gauged $U(1)$ with the vector made massive via Higgsing with an axion. The latter necessarily couples to instantons, and their action can be constrained, using both the electric and magnetic version of the axionic weak gravity conjecture, in terms of the cutoff of the theory. As a result, instanton-induced symmetry breaking operators with a suppression factor not smaller than $exp(-M_{rm P}^2/Lambda^2)$ are present, where $Lambda$ is a cutoff of the 4d effective theory. We provide a general argument and clarify the meaning of $Lambda$. Simple 4d and 5d models are presented to illustrate this, and we recall that this is the standard way in which things work out in string compactifications with brane instantons. The relation of our constraint to bounds that can be derived from wormholes or gravitational instantons and to those motivated by black-hole effects at finite temperature are discussed, and we present a generalization of the Giddings-Strominger wormhole solution to the case of a gauge-derived $U(1)$ global symmetry. Finally, we discuss potential loopholes to our arguments.
We develop methods for resummation of instanton lattice series. Using these tools, we investigate the consequences of the Weak Gravity Conjecture for large-field axion inflation. We find that the Sublattice Weak Gravity Conjecture implies a constraint on the volume of the axion fundamental domain. However, we also identify conditions under which alignment and clockwork constructions, and a new variant of N-flation that we devise, can evade this constraint. We conclude that some classes of low-energy effective theories of large-field axion inflation are consistent with the strongest proposed form of the Weak Gravity Conjecture, while others are not.
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