Consistency of the dual formulation of axion solutions to the strong CP problem

Abstract

An exact duality between axion with arbitrary potential and antisymmetric form-field has been derived some time ago. Using this duality, the axion solution to strong-CP problem has been formulated as a gauge invariant theory of forms. In this description, the QCD axion is represented by a Kalb-Ramond field which is eaten-up by the Chern-Simons $3$-form of QCD, thereby making it massive. This ensures the CP-invariance of the vacuum. Although viewed as an effective low energy theory, this formulation accomplishes the same goal as ordinary Peccei-Quinn mechanism, due to its gauge invariance, it is protected against unwanted UV-corrections. In the previous work it has been shown that dual formulation is insensitive to UV-physics in the sense that the corrections to CP-conserving vacuum from arbitrary massive sources are strictly zero. By going carefully through duality transformations and source-resolution, we reproduce this curious result and give some further consistency checks. We apply similar analysis to other approaches to naturalness problems based on form fields and axions, such as cosmological relaxation of the standard model Higgs boson mass via the attractor mechanism.