Planckian axions in string theory

A bstract We argue that super-Planckian diameters of axion fundamental domains can arise in Calabi-Yau compactifications of string theory. In a theory with N axions θ i , the fundamental domain is a polytope defined by the periodicities of the axions, via constraints of the form − π N constraints, while for P = N the diameter is further enhanced by eigenvector delocalization to N 3/2 f N . We directly verify our results in explicit Calabi-Yau compactifications of type IIB string theory. In the classic example with h 1,1 = 51 where parametrically controlled moduli stabilization was demonstrated by Denef et al. in [ 1 ], the largest metric eigenvalue obeys f N ≈ 0.013 M pl . The random matrix analysis then predicts, and we exhibit, axion diameters ≈ M pl for the precise vacuum parameters found in [ 1 ]. Our results provide a framework for pursuing large-field axion inflation in well-understood flux vacua.