Existence and physical realization of mixed fractional-instanton couplings

Determine whether mixed axion–gauge couplings involving fractional instantons—specifically terms proportional to θ·w2^s ∧ w2^{s′} mixing distinct PSU(N) sectors and terms proportional to θ·w2^s ∧ F2^i mixing PSU(N) and U(1) sectors—can exist and be realized in four-dimensional quantum field theories or in extra-dimensional UV completions of axion theories; and, if they do, characterize their implications for non-invertible symmetry structures and whether they can distinguish 4d from extra-dimensional axion theories.

Background

In the paper’s general treatment of axions coupled to multiple gauge sectors, the authors analyze non-invertible symmetries arising from ABJ anomalies with multiple U(1) and non-abelian (PSU(N)) factors. For fractional instantons associated with PSU(N), they restrict attention to diagonal couplings of the axion to each sector via w2 ∧ w2 terms, which are known to be consistent.

They explicitly note uncertainty about the possibility of cross-sector mixed terms between different w2 classes and between w2 and U(1) field strengths. Establishing the existence and physical realizability of such mixed couplings is important for a complete classification of anomaly structures that generate non-invertible symmetries and could shed light on differences between purely 4d axion models and extra-dimensional UV completions.