# MS Seminar (Mathematics - String Theory)

Speaker: Shigenori Nakatsuka (UTokyo) Feigin-Semikhatov conjecture and its applications Thu, Jan 21, 2021, 15:30 - 17:00 Zoom In this talk, we prove a Kazama-Suzuki type coset construction of the principal W-superalgebra of \$\mathfrak{sl}_{1|n}\$ from the subregular W-algebra of \$\mathfrak{sl}_n\$ and its inverse construction. The case \$n=2\$ recovers the original Kazama-Suzuki coset construction of the \$N=2\$ superconformal algebra from the affine vertex algebra of \$\mathfrak{sl}_2\$ and its inverse construction due to Feigin-Semikhatov-Tipunin. These two constructions imply that the Heisenberg cosets of these two (super)algebras are isomorphic, which has been conjectured by Feigin-Semikhatov and recently by Gaiotto-Rapcak. As an application, we determine the level when the principal W-superalgebra of \$\mathfrak{sl}_{1|n}\$ gives a rational superconformal field theory, classify the irreducible modules and determine the fusion rules from the corresponding results for the subregular W-algebra.