Repulsive forces and the weak gravity conjecture

Abstract

The Weak Gravity Conjecture is a nontrivial conjecture about quantum gravity that makes sharp, falsifiable predictions which can be checked in a broad range of string theory examples. However, in the presence of massless scalar fields (moduli), there are (at least) two inequivalent forms of the conjecture, one based on charge-to-mass ratios and the other based on long-range forces. We discuss the precise formulations of these two conjectures and the evidence for them, as well as the implications for black holes and for "strong forms" of the conjectures. Based on the available evidence, it seems likely that both conjectures are true, suggesting that there is a stronger criterion which encompasses both. We discuss one possibility. B Toroidal compactification of the heterotic string 50 1 IntroductionThe Weak Gravity Conjecture (WGC) [1] is most often motivated by a statement about black holes: if all subextremal black holes in a given quantum gravity are kinematically unstable, then conservation of charge and energy imply that there is some charged particle in the spectrum of the theory whose charge-to-mass ratio is at least as large as that of an extremal black hole. The WGC postulates that such a particle exists. This conjecture is intrinsically about gravitational theories, and goes by the slogan "gravity is the weakest force," meaning that gravitational interactions are insufficient to make a stable bound state (the black hole).However, there is another version of the conjecture, originating in [1] but emphasized more recently by Palti [2]: there is a charged particle with the property that two copies of the particle repel each other when they are far apart (a "self-repulsive" particle). In other words, the long-range repulsive gauge force between the two identical particles must be at least as strong as the combination of all long-range attractive forces between them. We will call this conjecture (and its generalizations) the "Repulsive Force Conjecture" (RFC).How does the Repulsive Force Conjecture relate to the Weak Gravity Conjecture as formulated in the first paragraph? If we assume that the only long-range forces are gravity and electromagnetism, then the RFC requires a charged particle with chargeto-mass ratio greater than or equal to some critical value (to ensure that the electromagnetic repulsion between two copies is stronger than their gravitational attraction). It is straightforward to check that the long-range force between two extremal Reissner-Nordström black holes vanishes; therefore, the critical ratio is exactly the charge-tomass ratio of an extremal Reissner-Nordström black hole. In other words, the RFC and the WGC are the same conjecture under these assumptions.Notice, however, that the RFC can be stated without specifically referring to gravity. This is an important distinction, because long range attractive interactions can also be mediated by massless scalar fields. This has two consequences: (1) in quantum gravities with massless scalars, the RFC and the WGC, as defined above, are not id...

A note on membrane interactions and the scalar potential

“…(2.23). As advertised, this extremal form of the WGC, which was originally formulated from extremality arguments for BH's, can be obtained from the requirement that the force between charged objects cancels exactly (see also [36,37,48,49] for more on this approach or [51] for an alternative approach to the WGC in terms of pair production). Let us remark that the action considered at the beginning of this section is really meaningful in D = 10, since in this case it is a piece of the 10d type II effective action coupled to Dp-branes.…”

“…This is just a manifestation of the special case in which arguments about force cancellation and extremality of black hole solutions coincide (for a more detailed discussion on the (in)equivalence of these two approaches see[36,37,48,49]). …”

A Tower Weak Gravity Conjecture from Infrared Consistency

“…Requiring consistency under dimensional reduction suggests that a bound on the charge‐to‐mass vectors has to be satisfied by the whole charge lattice. This stronger version of the WGC was subsequently shown to not always hold, though there are examples in string theory where the particles satisfying the WGC occupy a proper sub‐lattice …”

Swampland constraints on no-boundary quantum cosmology

“…Alternative possibilities include multi-field dynamics[35,49], excited initial conditions[51,54], and warm inflation[55,56].3 Scalar weak gravity conjecture (scalar WGC)[69] and its variants[70,71] are another class of Swampland conjectures which may be relevant. However, the presence of many variants implies there is no clear guiding principle.…”