What is the Magnetic Weak Gravity Conjecture for Axions?

TL;DR

The paper investigates whether axions with super-Planckian decay constants $f$ can satisfy a magnetic version of the Weak Gravity Conjecture by examining magnetically charged strings in four dimensions. It analyzes static Cohen–Kaplan strings (found to be singular for $f> M_P$), dynamical Gregory-type solutions that avoid singularities but require horizons, and topological-inflation scenarios as possible UV completions, as well as a two-axion winding construction to engineer an effective $f_{ ext{eff}}$ beyond $M_P$. It finds that the effective-string approach tends to yield tensions $T_{ ext{eff}}\sim f_{ ext{eff}}^2$, often super-Planckian, complicating a clean magnetic-WGC realization; backreaction considerations also indicate that pseudo-axion field ranges remain bounded, limiting trans-Planckian excursions. Overall, the work suggests that, under multiple reasonable definitions of the minimally charged object and reasonable UV completions, large-$f$ axions face substantial obstacles, with the final verdict depending sensitively on the allowed dynamics and interpretation of the magnetic object.

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 fundamental 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.

Figures (7)

• Figure 1: Cutoff scales of a weakly coupled gauge theory in the presence of gravity.
• Figure 2: The angle $\phi$ defined in (\ref{['angledef']}) is shown as a function of the coordinate $u$ for $f\approx 0.71M_\text{P}$ ($u_0\approx 4$) and $f\approx 1.56M_\text{P}$ ($u_0\approx0.83$). The shaded green area indicates the coordinate and angle range where one can visualize the space locally as conical, with a positive deficit angle (for $f\approx 0.71M_\text{P}$). $u=0$ corresponds to the outer singularity while the string center sits at $u=\infty$. The right intersection point of the blue and black dashed line at $u=u_+$ is roughly the core radius. For $f\approx 1.56M_\text{P}$ the angle is always larger than $2\pi$.
• Figure 3: Embedding of a 2-dimensional slice of the spacetime for an inflating global monopole in Euclidean 3-space. The upper part of the 'balloon' contains the inflating region.
• Figure 4: Winding effective field space of total length $\sim Nf$ (shown for $N=5$).
• Figure 5: The string type 1 is shown with one domain wall attached to it. The jump of $F_0$ across the wall is indicated.