MS Seminar (Mathematics - String Theory)

Speaker: Shigenori Nakatsuka (UTokyo)
Title: Feigin-Semikhatov conjecture and its applications
Date: Thu, Jan 21, 2021, 15:30 - 17:00
Place: Zoom
Abstract: 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.