On the 3-form formulation of axion potentials from D-brane instantons

The study of axion models and quantum corrections to their potential has experienced great progress by phrasing the axion potential in terms of a 3-form field eating up the 2-form field dual to the axion. Such reformulation of the axion potential has been described for axion monodromy models, and for axion potentials from non-perturbative gauge dynamics. In this paper we propose a 3-form description of the axion potentials from non-gauge D-brane instantons. Interestingly, the required 3-form field does not arise in the underlying geometry, but rather shows up in the KK compactification in the generalized geometry obtained when the backreaction of the D-brane instanton is taken into account.