Vertex operators for algebras and superalgebras

Supersymmetry and homogeneity of M-theory backgrounds

“…The Killing superalgebra of the above solution must be a sub-superalgebra of the superalgebra osp(8|2, R) corresponding to AdS 4 × S 7 . In fact, it is not hard to see that the superalgebra is u(1) ⊕ osp(6|2, R), which is a regular maximal sub-superalgebra of osp(8|2, R) [51]. This means that only the su( 4) is generated by Killing spinors, but since this acts transitively on S 7 , and will continue to do so on S 7 / , we see that also in this case supersymmetry is responsible for homogeneity.…”

Generators of Supersymmetric Classical W-Algebras

“…Looking for sl(1|2) principal embeddings, one is restricted to sl(n + 1|n). Moreover we note that the osp(3|2) superalgebra can be viewed as the folding of a sl(3|2) superalgebra, in the same way osp(1|2) can be viewed as the folding of sl(1|2) [13]. Then, embeddings of sl(3|2) superalgebras in sl(n + 1|n) looks like the more promising direction to study N = 3 SUSY W -algebras.…”

Superspin chains from superstring theory

“…Our notation might remind the reader of Kac-Dynkin diagrams for Lie superalgebras [84], for example, the Kac-Dynkin diagram corresponding to (0.12) is the following…”