# GTM seminar

Speaker: Naoki Genra (Kavli IPMU) Dualities on W-algebras and W-superalgebras Thu, Jul 15, 2021, 13:30 - 15:00 Zoom 2676.pdf We prove duality isomorphisms between Heisenberg cosets of subregular W-algebras and Heisenberg cosets of principal W-superalgebras. The simplest case is the isomorphism between the parafermion vertex algebras and the Heisenberg cosets of the $N=2$ superconformal vertex superalgebras. We also prove Kazama-Suzuki type dualities between subregular W-algebras and W-superalgebras, and derive blockwise correspondences of module categories through relative semi-infinite cohomologies. Feigin-Semikhatov first conjectured these results and Gaiotto-Rapčák recently conjecture generalizations of them, namely trialities of Y-algebras. While Creutzig-Linshaw prove lots of these conjectures by using $W_{1+\infty}$-algebras, we use screening operators. We will explain the relationship between them and relate to Rapčák-Soibelman-Yang-Zhao¡Çs W-algebras. This is joint work with Thomas Creutzig, Shigenori Nakatsuka and Ryo Sato.