Cohomology of Twisted Rota-Baxter operator on Associative Conformal Algebra

In this paper, we investigate twisted Rota-Baxter (TRB) operators on associative conformal algebras. We construct an L ∞ -algebra whose Maurer-Cartan elements correspond precisely to H-twisted Rota-Baxter (H-TRB) operators. Utilizing this characterization, we develop a cohomology theory for conformal H-TRB operators. We prove that this cohomology is isomorphic to the Hochschild cohomology of a specific associative conformal algebra with coefficients in a conformal bimodule. Furthermore, we apply this theory to study linear and formal deformations of conformal H-TRB operators. We identify the infinitesimal of a deformation as a 1-cocycle and establish a sufficient condition for rigidity in terms of Nijenhuis elements.