Planckian axions in string theory

Abstract

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 < Q i j θ j < π. We compute the diameter of the fundamental domain in terms of the eigenvalues f 2 1 ≤ . . . ≤ f 2 N of the metric on field space, and also, crucially, the largest eigenvalue of (QQ ) −1 . At large N , QQ approaches a Wishart matrix, due to universality, and we show that the diameter is at least N f N , exceeding the naive Pythagorean range by a factor > √ N . This result is robust in the presence of P > 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 ≈ 0.013M 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.

Transplanckian axions!?

“…The 'empirical' case-by-case realization that this requirement is not obviously realized in string theory compactifications [7] (which provide a template for a quantum gravity framework), motivated the construction of models with multiple axions and potentials from gauge instantons, in which some axion linear combination effectively hosts a transplanckian field range in its basic period, even if the original periodicities are taken sub-planckian [8,9] (see [10][11][12][13][14][15][16][17][18][19] for recent works). These models are formulated in purely phenomenological field theory terms, and therefore there remains the question of whether their features survive in actual embeddings in theories including quantum gravitational corrections.…”

“…It has been argued that suitable cancellations can occur such that even if a parametrically large field range is not possible, one might still get a sufficient large field range to provide inflation. Studies regarding the diameters of JHEP08 (2015)032 axion moduli spaces in Calabi-Yau manifolds have been carried out in [21], showing the difficulties arising to have an enhancement of a moduli space diameter while keeping the overall volume small (see also [17] for a more optimistic view). We just want to remark that the gravitational effects which are usually argued to be behind the difficulties from getting transplanckian field ranges in string theory might actually be suppressed for the case of multiple axions.…”

On axionic field ranges, loopholes and the weak gravity conjecture

“…The vector indices on c, Q k run over all axions, of which there are N , while the index k runs over a set of instantons which is assumed to satisfy the CHC (this automatically implies that M ≥ N and guarantees the eventual stabilization of all axions). Now, a general Lagrangian of the form (2.1) may be quite complicated and the notion of an 'axion decay constant' is somewhat ambiguous [13]. It is nevertheless useful to have a quick diagnostic tool in order to determine at a glance when inflation may occur.…”

Tunneling in axion monodromy

“…Despite the existence of loopholes, these results create substantial obstacles for many models of axionic inflation and may explain why the thorough investigations of [9,10] have not succeeded in finding a large field model which violates WGC motivated bounds.…”

“…9 In addition to choosing an initial solution, there may also be multiple choices of how to analytically continue the Euclidean solution φ i into a Lorentzian solution. The choice of continuation and the solution together determine the initial conditions in Lorentzian space.…”