Towards Kac-van de Leur Conjecture: locality of superconformal algebras.

par Yuly BILLIG

jeudi 12 mars 2020, 15:15 → 16:15 Europe/Paris

112 (bât. Braconnier)

Superconformal algebras are simple Lie superalgebras with a centerless Virasoro subalgebra which are Z-graded by the Cartan element of the Virasoro and have a global bound on the dimensions of components. Superconformal algebras play an important role in Conformal Field Theories. Kac and van de Leur gave a conjectural list of superconformal algebras. We will review progress made towards this classification by Fattori-Kac and Kac-Lau-Pianzola. These partial results were obtained under an additional assumption of locality. Using the machinery of cuspidal modules developed by Billig-Futorny, we prove that superconformal algebras are indeed local.