On the Possibility of Large Axion Moduli Spaces

TL;DR

The paper investigates whether axion moduli spaces in string theory can attain large field ranges sufficient for high-scale inflation. It derives a rigorous bound for the axion radius in Type IIB Calabi-Yau compactifications with simplicial Kähler cones and shows non-simplicial cones introduce extra potential terms that generally cap the accessible field range. A statistical study using toric Calabi-Yau data indicates no parametric enhancement of the moduli-space diameter and reveals the pervasive impact of additional instanton terms when non-simplicial cones are involved. The authors connect these geometric constraints to the weak gravity conjecture, arguing that large axion moduli spaces are disfavored in any consistent theory of quantum gravity, with implications for natural inflation and multi-axion scenarios across corners of the duality web.

Abstract

We study the diameters of axion moduli spaces, focusing primarily on type IIB compactifications on Calabi-Yau three-folds. In this case, we derive a stringent bound on the diameter in the large volume region of parameter space for Calabi-Yaus with simplicial Kähler cone. This bound can be violated by Calabi-Yaus with non-simplicial Kähler cones, but additional contributions are introduced to the effective action which can restrict the field range accessible to the axions. We perform a statistical analysis of simulated moduli spaces, finding in all cases that these additional contributions restrict the diameter so that these moduli spaces are no more likely to yield successful inflation than those with simplicial Kähler cone or with far fewer axions. Further heuristic arguments for axions in other corners of the duality web suggest that the difficulty observed in hep-th/0303252 of finding an axion decay constant parametrically larger than $M_p$ applies not only to individual axions, but to the diagonals of axion moduli space as well. This observation is shown to follow from the weak gravity conjecture of hep-th/0601001, so it likely applies not only to axions in string theory, but also to axions in any consistent theory of quantum gravity.

Figures (9)

• Figure 1: A subset of a (non-simplicial) Mori cone (left) is dual to a superset of the (also non-simplicial) Kähler cone (right), and vice versa.
• Figure 2: The fraction of toric varieties with non-simplicial Kähler cone as a function of $N=h^{1,1}$ quickly approaches 1.
• Figure 3: The average value of $\tilde{f} = \pi \sqrt{N} f$ is shown in black, with error bars indicating the standard deviation over the sample of Calabi-Yaus studied. Here, $f$ is the square root of the largest eigenvalue of the metric $G_{ij}^b$. The maximum $\tilde{f}$ at each $N$ is shown in red. The average does not vary greatly with $N$.
• Figure 4: The average value of $\tilde{f} / g_s = \pi \sqrt{N} f / g_s$, where $f$ is the square root of the largest eigenvalue of the metric $G_{ij}^\vartheta$, is shown in black, with error bars indicating the standard deviation over the sample of Calabi-Yaus studied. The maximum $\tilde{f}$ at each $N$ is shown in red. The average decreases with increasing $N$.
• Figure 5: The largest effective radius of axion moduli space for each $N$ is shown. Once we account for additional contributions to the potential arising in compactifications on Calabi-Yaus with non-simplicial Kähler cone, the effective range accessible to the axions is cut off (compare with Figure \ref{['baxionplot']}). In all simulated axion moduli spaces considered, the effective radius is cut down to less than $\pi \, M_p$, well within the bound (\ref{['rbound']}) derived in the simplicial case.