All chiral W -algebra extensions of so (2, 3)

A bstract We show that there are four chiral W W -algebra extensions of so (2, 3) so 2 3 algebra and construct them explicitly. We do this by a simple identification of each of the inequivalent embeddings of a copy of sl (2, R) sl 2 ℝ in the so (2, 3) so 2 3 algebra and the maximal subalgebra h h that commutes with it. Then using the standard 2d chiral CFT techniques we find the corresponding W W -algebra extensions. Two of the four resultant W W -algebras are new, one of which may be thought of as the conformal bms₃ bms 3 algebra valid for finite values of its central charge.