Axions, Three-Forms, and M-Theory

TL;DR

The paper addresses UV-completing axions by geometrizing the axion as the brane-position mode of a charged 3-brane in a (4+1)-D setting, where the shift symmetry emerges from a residual 5D diffeomorphism. Mass generation occurs through couplings to higher-form fields, notably a three-form Higgs mechanism, and the construction is embedded in M-theory, revealing a dual two-form on the boundary of an open membrane and a D3-brane realization in string theory. The authors provide a detailed effective field theory (EFT) treatment, derive the axion mass formula $m_{\text{axion}} = \dfrac{\mathcal{Q}}{\sqrt{\\pi \\ R \\ \\mathcal{T}}}$, and show how flux quantization induces a multi-valued potential and a discrete gauge symmetry, akin to axion monodromy. The M-theory uplift clarifies the open-string axion picture, connects the EFT to an open-membrane description, and offers a UV-complete perspective with potential cosmological and phenomenological implications for axion-like particles.

Abstract

Scalar fields with masses protected by global shift symmetries, commonly referred to as axions, are abundantly used in effective field theories in cosmology and particle physics. However, global symmetries cannot be expected to be protected at the fundamental level. Finding consistent ultra-violet completions for axions is therefore a necessity. In this work, we identify the axion with the position mode of a charged 3-brane in (4+1)-dimensions. The shift symmetry of the axion is then a residual diffeomorphism in the fifth dimension orthogonal to the brane. Meanwhile, the brane is coupled to a flux in the fifth dimension. From the (3+1)-dimensional perspective, this construction generates (perturbatively) a mass for the axion and matches previously known proposals in the literature based on the coupling between the axion and a three-form gauge field. In a second step, we uplift this (4+1)-dimensional model to M-theory, where the same three-form is found to couple to the membrane with a (2+1)-dimensional worldvolume. In particular, our proposal also elucidates the duality between the axion and a two-form gauge field in the literature. We show that this dual two-form couples to the boundary of an open membrane in M-theory. Finally, we comment on the relations to and differences from other closed and open string axion monodromy models.

Figures (4)

• Figure 1: Axion as a brane-bending mode from the shape of a 3-brane in the fifth extra dimension, which is compactified on a circle.
• Figure 2: The string and M-theory uplift of the axion universe. From the string theory perspective, the axion is an open string mode that perturbs the shape of the D3-brane. From the M-theory perspective, the axion is dualized to be a differential two-form potential $\mathbb{A}^{\!(2)}$, and it is coupled to open M2-branes that end on an M5-brane.
• Figure 3: An illustration of the antipodal two-brane configuration. Our universe as a 3-brane sits at $y=0$ and its anti-brane at $y = \pi \, R$ , with $y$ the compactified dimension that is orthogonal to the brane. These two branes carry the same charge $\mathcal{Q}$ but with opposite signs. The background value of the four-form field strength $\bar{H}_{01234}$ is a discontinuous function in $y$, which is equal to $q_\text{S}$ in the southern semi-circle and $q_\text{N}$ in the northern semi-circle.
• Figure 4: The potential of the axion is multivalued, satisfying a discrete (residual) gauge symmetry with periodicity $f$.