Constraints on Axion Inflation from the Weak Gravity Conjecture

TL;DR

The paper examines whether axion inflation driven by decay-constant alignment can be embedded in string theory without conflicting with quantum-gravity principles. By analyzing type IIB Calabi–Yau compactifications, nef/effective cone geometry, and the generalized Weak Gravity Conjecture, it shows that simple alignment usually cannot extend the inflaton range beyond $\mathcal{O}(M_p)$ and anti-alignment is incompatible with sustained inflation in typical setups. It also evaluates a D7-brane–driven alignment scenario, finding it potentially bypasses some bounds but introduces stringent geometric and model-building constraints. Overall, the work suggests that while alignment-based natural inflation faces significant hurdles in string theory, there may be narrow, highly-tuned routes or alternative mechanisms (e.g., monodromy or D7-dominated potentials) that could still realize viable inflation under precise conditions.

Abstract

We derive constraints facing models of axion inflation based on decay constant alignment from a string-theoretic and quantum gravitational perspective. In particular, we investigate the prospects for alignment and `anti-alignment' of $C_4$ axion decay constants in type IIB string theory, deriving a strict no-go result in the latter case. We discuss the relationship of axion decay constants to the weak gravity conjecture and demonstrate agreement between our string-theoretic constraints and those coming from the `generalized' weak gravity conjecture. Finally, we consider a particular model of decay constant alignment in which the potential of $C_4$ axions in type IIB compactifications on a Calabi-Yau three-fold is dominated by contributions from $D7$-branes, pointing out that this model evades some of the challenges derived earlier in our paper but is highly constrained by other geometric considerations.

Figures (5)

• Figure 1: The effective cone (red) is spanned by two irreducible effective divisors. The nef cone (blue) is contained in the closure of the effective cone. 'Anti-alignment' occurs if the angle $\theta$ between $\tilde{D}_1$ and $\tilde{D}_2$ approaches $\pi$.
• Figure 2: When two irreducible divisors are anti-aligned at an angle just less than $\pi$, the field range is stretched so that the greatest displacement occurs when $\vartheta_1$ and $\vartheta_2$ have the same sign (left). When the irreducible divisors are aligned an an angle of about $\pi$, the greatest displacement occurs when the two axions have opposite sign (right).
• Figure 3: When the generators of the effective cone (shown in red) are not aligned, it is possible for the effective cone to be simplicial and still contain the nef cone (shown in blue) (left). However, if two generators of the effective cone are approximately aligned, the effective cone must be non-simplicial, which means that there will be additional instanton contributions to the axion potential.
• Figure 4: The angle between the charge vectors approaches $\pi$ for anti-alignment (left) and $0$ for alignment (right). The requirement that the convex hull spanned by the vectors and their negatives should contain the unit ball restricts the maximum displacement of the inflaton to be $\lesssim \pi M_p$.
• Figure 5: A model with three charge vectors and two axions. Although the generalized weak gravity conjecture still constrains the size of moduli space, one could conceivably achieve a large inflaton traversal by taking $\theta \rightarrow 0$ as long as the potential contributions from $\vec{z}_3$ dominate those from $\vec{z}_2$, thereby allowing multiple traversals of the $\phi_2$ axion moduli space.