Abstract
Abstract
We show that there are four chiral $$ \mathcal{W} $$
W
-algebra extensions of $$ \mathfrak{so}\left(2,3\right) $$
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 $$ \mathfrak{sl}\left(2,\mathbb{R}\right) $$
sl
2
ℝ
in the $$ \mathfrak{so}\left(2,3\right) $$
so
2
3
algebra and the maximal subalgebra $$ \mathfrak{h} $$
h
that commutes with it. Then using the standard 2d chiral CFT techniques we find the corresponding $$ \mathcal{W} $$
W
-algebra extensions. Two of the four resultant $$ \mathcal{W} $$
W
-algebras are new, one of which may be thought of as the conformal $$ {\mathfrak{bms}}_3 $$
bms
3
algebra valid for finite values of its central charge.
Publisher
Springer Science and Business Media LLC