  (Tri)dendriform algebras, Rota-Baxter operators, and closely related
NS-algebras have a number of dominant applications in physics, especially in
quantum field theory. Proceeding from the recent study relating these
structures, this paper considers (tri)dendriform algebras, NS-algebras, and
(twisted)Rota-Baxter operators in the context of BiHom-associative conformal
algebras. A comprehensive investigation of the BiHom-(tri)dendriform conformal
algebras and their characterization in terms of conformal bimodule has been
conducted. The study of BiHom-NS-conformal algebra reveals that it is not only
a generalization of NS-conformal algebra using two structural maps but is also
the generalization of BiHom-(tri)dendriform conformal algebras. Additionally,
it is found to have a close proximity between BiHom-twisted Rota-Baxter
operators and BiHom-NS-conformal algebras. The comparative study to Rota-Baxter
operators on BiHom-associative conformal algebras and Rota-Baxter operators on
BiHom-(tri)dendriform conformal algebras reveals a relationship between
BiHom-quadri conformal algebra and Rota-Baxter operators. In the end, the
concept of Rota-Baxter system (a generalization of the Rota-Baxter operator)
for BiHom-associative conformal algebras and BiHom-dendriform conformal
algebras is narrated, where the interconnections of these algebras are
depicted. Furthermore, a connection is established between BiHom-quadri
conformal algebras and Rota-Baxter systems for BiHom-dendriform conformal
algebras.
