Abstract: |
Given a simple Lie superalgebra, an even nilpotent element and a complex number (called the level), we can define a vertex superalgebra called a W-superalgebra in the sense of Kac-Roan-Wakimoto. The best studied ones are principal W-algebras which are associated with a simple Lie algebra and a principal nilpotent element. They enjoy the so-called Feigin-Frenkel duality, which is an isomorphism between principal W- algebras if their original Lie algebras are Langlands dual and their levels satisfy a certain relation. Now a days, this duality is understood as a consequence of S-duality in the 4d theory. In this talk, we show that the Heisenberg cosets of subregular W-algebras and principal W-superalgebras enjoy a similar duality, and moreover, that these two algebras are obtained from each other by Kazama-Suzuki type coset constructions. This is based on a joint work with T. Creutzig and N. Genra. |