Axions, Higher-Groups, and Emergent Symmetry

TL;DR

The article analyzes axions with higher-form global symmetries and shows these extend into nontrivial higher-group structures when coupled to gauge sectors. By introducing background fields for these symmetries, the authors derive flux relations, reveal fractional four-form fluxes $G^{(4)}$ and $H^{(3)}$, and formulate anomaly inflow conditions that couple different form degrees. They then derive universal inequalities on the scales at which emergent symmetries appear in UV completions, notably $E_{ ext{screen}}\lesssim E_{ ext{string}}$ for axion-Yang-Mills and analogous bounds for axion-QCD and axion electrodynamics, including adjoint Higgsing realizations. These results constrain UV couplings and the viability of EFTs describing long-distance axion physics, ensuring consistency between the emergence of higher-form and zero-form symmetries in RG flows. The framework provides model-independent checks relevant to KSVZ-like constructions and broader axion phenomenology.

Abstract

Axions, periodic scalar fields coupled to gauge fields through the instanton density, have a rich variety of higher-form global symmetries. These include a two-form global symmetry, which measures the charge of axion strings. As we review, these symmetries typically combine into a higher-group, a kind of non-abelian structure where symmetries that act on operators of different dimensions, such as points, lines, and strings, are mixed. We use this structure to derive model independent constraints on renormalization group flows that realize theories of axions at long distances. These give universal inequalities on the energy scales where various infrared symmetries emerge. For example, we show that in any UV completion of axion-Yang-Mills, the energy scale at which axion strings can decay is always larger than the mass scale of charged particles.

Figures (2)

• Figure 1: A junction where zero-form symmetry defects of type ${\bf g}$, ${\bf h}$, ${\bf k}$, ${\bf g}{\bf h}{\bf k}\in G$ meet in codimension three. This configuration is generic in spacetime dimension three and above. The junctions of three codimension-one defects are in red, and their intersection is the black point. At the codimension-three intersection, a one-form symmetry defect $\beta({\bf g},{\bf h},{\bf k})$ emanates, signaling the 2-group symmetry. In $d$ dimensions, all objects span the remaining $d-3$ dimensions.
• Figure 2: This figure illustrates how the axion string can unwind. In (a), we show the winding solution for the axion string along a circle of fixed radius. As we go around the blue circle (a circle linking the axion string (black) in spacetime) the scalar field $\varphi$ winds around the bottom of the mexican hat potential in red. (b) shows the excitations of the radial mode which is activated at the scale $m_\rho \sim m f$. (c-e) shows a process by which we can unwind the scalar field. Here we deform solution in the radial direction over the top of the potential which costs energy $\sqrt{m}f>>m f$. The resulting configuration has no winding -- indicating the decay of the string.