Comment on "Geometry of the Grosse-Wulkenhaar model"

We clarify a key point in the geometric reinterpretation of the Grosse$\text{unicode}x2013$Wulkenhaar (GW) model proposed in “Geometry of the Grosse-Wulkenhaar model” [JHEP 03 (2010) 053]. Specifically, we show that the analysis in Section 6 was performed not for the actual $\mathrm{\Omega }$-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$\text{unicode}x2014$relating the harmonic potential term to background curvature$\text{unicode}x2014$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.