The Weak Gravity Conjecture holds that gravity must be the weakest force. This is true of the familiar forces in our own universe -- electromagnetism, for instance, is many orders of magnitude stronger than gravity. But the bold claim of the Weak Gravity Conjecture is that this statement is true, not only for electromagnetism in our universe, but for any similar force in any consistent universe governed by quantum mechanics. In this brief introduction, aimed at advanced undergraduates or beginning graduate students, we elaborate on the precise definition of the Weak Gravity Conjecture, the evidence for it, and some of the remarkable implications of it. We explain how the Weak Gravity Conjecture may play a role in bridging the gulf between the formal mathematics of string theory and the real-world observations of particle physics and cosmology.
We study the Weak Gravity Conjecture in the presence of scalar fields. The Weak Gravity Conjecture is a consistency condition for a theory of quantum gravity asserting that for a U(1) gauge field, there is a particle charged under this field whose mass is bounded by its charge. It was extended to a statement about any canonical pair of (p - 1)-dimensional object and p-form coupling to it, in particular to axion-instanton pairs. The gauge-scalar Weak Gravity Conjecture is a modification of this bound that includes scalar interactions. We propose a similar extension to cases where scalar fields …
In four-dimensional axion electrodynamics, a Chern-Simons coupling of the form $θF \wedge F$ leads to a higher-group global symmetry between background gauge fields. At the same time, such a Chern-Simons coupling leads to a mixing between the Weak Gravity Conjectures for the axion and the gauge field, so that the charged excitations of a Weak Gravity Conjecture-satisfying axion string will also satisfy the Weak Gravity Conjecture for the gauge field. In this paper, we argue that these higher-group symmetries and this phenomenon of Weak Gravity Conjecture mixing are related to one another. We s…
Motivated by the Weak Gravity Conjecture, we uncover an intricate interplay between black holes, BPS particle counting, and Calabi-Yau geometry in five dimensions. In particular, we point out that extremal BPS black holes exist only in certain directions in the charge lattice, and we argue that these directions fill out a cone that is dual to the cone of effective divisors of the Calabi-Yau threefold. The tower and sublattice versions of the Weak Gravity Conjecture require an infinite tower of BPS particles in these directions, and therefore imply purely geometric conjectures requiring the exi…
We use type I string models with supersymmetry broken by compactification (à la Scherk-Schwarz) in order to test the weak gravity conjecture in the presence of runaway potentials in a perturbative string theory setting. For a finite value of the supersymmetry breaking radius there is a runaway potential, which is the only possibility if one accepts the non-existence of de Sitter vacua. Although the weak gravity conjecture is valid in the decompactification limit, for fixed values of the radius we show that there are short-ranged attractive D1 brane-brane interactions. We argue however that at …
We analyze AdS and dS swampland conjectures in a three-dimensional higher spin theory with self-interacting matter, which contains conformal gravity and is almost topological. A theory of a similar type was proposed as the effective theory in the high energy phase of non-critical M-theory in 3D. With some details differing from the usual string theory story, it is found that the resulting effective theory, namely topologically massive gravity, fits well into the web of the proposed swampland conjectures. Supporting a recent proposal, in particular we find that this 3D theory gives rise to a qu…
We show that compactifications of the heterotic string on a circle exhibit at the boundary of moduli space ($R\to 0$, or equivalently the decompactification limit $R \to \infty$) a tower of winding or momentum modes that enhance the $E_8 \times E_8$ or $SO(32)$ gauge symmetry to the affine algebras $(E_9 \oplus E_9)/\sim$ (the identification means that the two copies of $E_9$ share the same central extension) and $\hat{D}_{16}$, respectively. We also prove that these towers of modes satisfy the lattice Weak Gravity and Repulsive Force Conjectures.
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 theor…
We explore the notion of approximate global symmetries in quantum field theory and quantum gravity. We show that a variety of conjectures about quantum gravity, including the weak gravity conjecture, the distance conjecture, and the magnetic and axion versions of the weak gravity conjecture can be motivated by the assumption that generalized global symmetries should be strongly broken within the context of low-energy effective field theory, i.e. at a characteristic scale less than the Planck scale where quantum gravity effects become important. For example, the assumption that the electric one…
We investigate the asymptotic Tower Weak Gravity Conjecture in weak coupling limits of open string theories with minimal supersymmetry in four dimensions, focusing for definiteness on gauge theories realized on 7-branes in F-theory. Contrary to expectations, we find that not all weak coupling limits contain an obvious candidate for a tower of states marginally satisfying the super-extremality bound. The weak coupling limits are classified geometrically in the framework of EFT string limits and their generalizations. We find three different classes of weak coupling limits, whose physics is char…
We study quantum corrections in four-dimensional theories with $N=1$ supersymmetry in the context of Quantum Gravity Conjectures. According to the Emergent String Conjecture, infinite distance limits in quantum gravity either lead to decompactification of the theory or result in a weakly coupled string theory. We verify this conjecture in the framework of $N=1$ supersymmetric F-theory compactifications to four dimensions including perturbative $α'$ as well as non-perturbative corrections. After proving uniqueness of the emergent critical string at the classical level, we show that quantum corr…
We study type IIA orientifold compactifications with fluxes that give rise to perturbatively stable, non-supersymmetric AdS$_4$ vacua with D6-brane gauge sectors. Non-perturbative instabilities can be mediated by D8-branes wrapped on the six internal dimensions $X_6$, if they reduce to 4d membranes with a charge $Q$ larger than its tension $T$. The mismatch $Q \neq T$ arises due to i) curvature corrections and ii) the BIon backreaction of D6-branes wrapping 3-cycles of $X_6$. We give a simple expression for the second effect in toroidal orientifolds, and find that only pairs of 3-cycles at SU(…
An alternative refined de Sitter conjecture giving rise to a natural combination of the first and second derivatives of the scalar potential was proposed recently by David Andriot and Christoph Roupec (Fortsch. Phys. 67 (2019) no.1-2, 1800105). In this work, we study the inflation models in a general scalar-tensor theory with exponential and hyperbolic tangent forms of potential as well as model with quantum corrected potential and examine whether these three models of inflation can satisfy this further refining de Sitter swampland conjecture or not. Regarding our analysis with proper choices …
Positivity of the gravitational path integral implies the axionic weak gravity conjecture
Leinweber Institute for Theoretical Physics and Department of Physics, University of California, Berkeley（加州大学伯克利分校莱因韦伯理论物理研究所与物理系）；RIKEN iTHEMS Center for Interdisciplinary Theoretical and Mathematical Sciences（理化学研究所 iTHEMS 跨学科理论与科学中心）；Joseph Henry Laboratories, Princeton University（普林斯顿大学约瑟夫·亨利实验室）；Department of Physics, Harvard University（哈佛大学物理系）
We search for a possible relation between weak gravity conjecture and conformal field theory in the hyperscaling violating and Kerr-Newman-AdS black holes. We deal with the critical points of the black hole systems through the correlation function introduced in conformal field theory. We discuss the weak gravity conjecture conditions by the imaginary part of the energy obtained from the critical points and their poles. Under the assumptions $z=1$, $d=1$ and $θ\rightarrow0^{-}$, we link weak gravity conjecture to the hyperscaling violating black holes due to the existence of $r_{H}$ larger and …
