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 [Formula: see text]-algebra whose Maurer–Cartan elements correspond precisely to [Formula: see text]-twisted Rota–Baxter ([Formula: see text]-TRB) operators. Utilizing this characterization, we develop a cohomology theory for conformal [Formula: see text]-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 [Formula: see text]-TRB operators. We identify the infinitesimal of a deformation as a [Formula: see text]-cocycle and establish a sufficient condition for rigidity in terms of Nijenhuis elements.