On the Possibility of Large Axion Moduli Spaces

TL;DR

This paper investigates the size of axion moduli spaces in string theory, deriving bounds and analyzing their implications for inflation and the weak gravity conjecture across different Calabi-Yau compactifications.

Contribution

It provides a new bound on axion moduli space diameters in type IIB Calabi-Yau compactifications with simplicial Kähler cones and explores restrictions from additional contributions, linking to the weak gravity conjecture.

Findings

Bound on axion moduli space diameter in large volume limit.

Additional contributions restrict the effective field range of axions.

Difficulty in achieving super-Planckian decay constants applies broadly, consistent with the weak gravity conjecture.

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 K\"ahler cone. This bound can be violated by Calabi-Yaus with non-simplicial K\"ahler 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 K\"ahler 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.