What is the magnetic Weak Gravity Conjecture for axions?

Abstract

The electric Weak Gravity Conjecture demands that axions with large decay constant f couple to light instantons. The resulting large instantonic corrections pose problems for natural inflation. We explore an alternative argument based on the magnetic Weak Gravity Conjecture for axions, which we try to make more precise. Roughly speaking, it demands that the minimally charged string coupled to the dual 2‐form‐field exists in the effective theory. Most naively, such large‐f strings curve space too much to exist as static solutions, thus ruling out large‐f axions. More conservatively, one might allow non‐static string solutions to play the role of the required charged objects. In this case, topological inflation would save the superplanckian axion. Furthermore, a large‐f axion may appear in the low‐energy effective theory based on two subplanckian axions in the UV. The resulting effective string is a composite object built from several elementary strings and domain walls. It may or may not satisfy the magnetic Weak Gravity Conjecture depending on how strictly the latter is interpreted and on the cosmological dynamics of this composite object, which remain to be fully understood. Finally, we recall that large‐field brane inflation is naively possible in the codimension‐one case. We show how string‐theoretic back‐reaction closes this apparent loophole of large‐f (non‐periodic) pseudo‐axions.

Instantons and infinite distances

“…in agreement with the magnetic version of the Weak Gravity Conjecture for axions [17,67] (see also [68]), with an intriguing extra factor of ρ. In this sense, one may interpret √ T D1…”

The Swampland: Introduction and Review

“…The magnetic Weak Gravity Conjecture should also have an analogous statement for axions. This was studied in []. In [], based on results in [], it was proposed that for an axion with decay constant f , there is a bound on the cutoff of the effective theory which takes the form There are some subtleties with this proposal, in particular the axion in question here should be an axion such that its associated string should have a singular core.…”

A holographic derivation of the weak gravity conjecture

“…This is only the mildest form of the conjecture. There are several more refined and constraining versions, such as a version applying to axions and other p-form fields, the Convex Hull Condition [47], Lattice and Tower WGC [48, 49], scalar versions of the conjecture [50-53] (leading to a connection to the Distance Conjecture and emergence [54-57]), and a variant leading to the instability of nonsupersymmetric AdS space [58, 59] (and to proposed constraints on the Standard Model [60-63]).Variants of the WGC have also been argued to constrain axion models of inflation or relaxation [48,58,[64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83]. The vanishing photon mass prediction mentioned above involves the WGC as well.All of this makes the WGC one of the most interesting Swampland constraints, but why should it be true?…”