Determine whether the Moyal-plane infrared divergence survives nonperturbative treatment

Determine whether the infrared divergence of the first-order interaction correction to entanglement entropy in the Moyal-plane limit persists after resummation or a non-perturbative treatment of the interaction contribution.

Background

In the Moyal-plane limit of the fuzzy disc, the free entanglement entropy remains finite, whereas the first-order correction grows proportionally to the total area of the disc and diverges as the disc radius tends to infinity. The perturbative expansion also becomes non-uniform in the matrix-size parameter, so fixed nonzero coupling eventually invalidates the first-order approximation.

The paper therefore leaves unresolved whether the volume-extensive infrared divergence is a genuine pathology of the interacting theory or instead signals the breakdown of naive perturbation theory. A non-perturbative analysis or suitable resummation is required to distinguish these possibilities.

References

Is the apparently extensive IR divergence of the first-order correction a genuine pathology of the interacting theory when formulated with fuzzy-space regularization, or does it merely signal the breakdown of naive perturbation theory and the need for a non-perturbative treatment of the interaction contribution to the EE? In particular, determining whether the IR divergence persists after a suitable resummation or non-perturbative treatment is essential for understanding its possible relation to the UV/IR mixing characteristic of noncommutative field theories.

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

To establish a genuine UV/IR mixing mechanism, one would ideally need to show that the $R2$ dependence in Eq.~EEcorDisc4 originates predominantly from the high spectral modes running in the loop. Although, as argued above and supported by our numerical results, the extensive contribution arises from summing an approximately constant contribution over all radial shells, it remains possible that the UV modes contribute substantially to an effect that ultimately grows as $R2$.

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