On the Possibility of Large Axion Moduli Spaces
  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. 
Tom Rudelius
hep-th