Comment on “Geometry of the Grosse–Wulkenhaar model”

In this paper, we clarify a key point in the geometric reinterpretation of the Grosse–Wulkenhaar (GW) model proposed in “Geometry of the Grosse–Wulkenhaar model” [J. High Energy Phys. 3 (2010) 53]. Specifically, we show that the analysis in Sec. 6 of that paper was performed not for the actual [Formula: see text]-term in the GW action, which involves both ordinary and star-products, but for a closely related term containing only star-products. Once corrected, the main conclusion — relating the harmonic potential term to background curvature — remains valid, though the parameter identification must be revised. This also resolves a discrepancy concerning the emergence of certain vacuum solutions in the self-dual limit of the model.