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We study the two-dimensional version of a quartic self-interacting quantumscalar field on a curved and noncommutative space (Snyder-de Sitter). We showthat the model is renormalizable at the one-loop level and compute the betafunctions of the related couplings. The renormalization group flow is thenstudied numerically, arriving at the conclusion that noncommutative-curveddeformations can yield both relevant and irrelevant contributions to theone-loop effective action.

The Snyder-de Sitter Scalar $\varphi^4_{\star}$ Quantum Field Theory in D=2