Identify the precise spectral mechanism producing the infrared divergence

Identify the precise spectral mechanism responsible for the infrared divergence of the first-order entanglement-entropy correction in the fuzzy-disc regularization.

Background

The correction is expressed as complicated sums over eigenvalues associated with different angular-momentum sectors, making an analytic determination of its dominant spectral contributions difficult. The authors note that increasingly ultraviolet-dominated sectors continue to contribute to the extensive divergence, but this observation does not establish the underlying mechanism.

A direct spectral decomposition of the correction is needed to determine whether ultraviolet modes generate the infrared-extensive behavior and whether it should be interpreted as UV/IR mixing. The current formulation does not provide that identification.

References

Nor does it provide a direct analytical way of identifying the precise mechanism responsible for the IR divergence. Nevertheless, we can still make some heuristic observations.

— Entanglement Entropy of Interacting Scalar Theories on Fuzzy Spaces  (2609.10027 - Allouche et al., 9 Sep 2026) in Section 5, Discussion