Comment on "Geometry of the Grosse-Wulkenhaar model"

We clarify a key point in the geometric reinterpretation of the Grosse-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 applied not to the actual $Ω$-term in the GW action, but to a closely related term involving a mixed use of ordinary and 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.