Equivalences between weight modules via $\mathcal{N}=2$ coset constructions

Abstract

In this paper we introduce a variant of weight modules for certain conformal vertex superalgebras as an appropriate framework of the $\mathcal{N}=2$ supersymmetric coset construction. We call them weight-wise admissible modules. Motivated by the work of Feigin-Semikhatov-Tipunin, we give (block-wise) categorical equivalences between the categories of weight-wise admissible modules over ${\widehat{\mathfrak{sl}}}_2$ and the $\mathcal{N}=2$ superconformal algebra, induced by the coset construction. As an application, we obtain some character formulae of modules over the $\mathcal{N}=2$ superconformal algebra.

25 pages, Remark 7.4 is corrected, references are added to Introduction, Remark 7.4, and Remark 7.14

References in corpus (1)

• Schur-Weyl Duality for Heisenberg Cosets

Cited by in corpus (4)

• Schur-Weyl Duality for Heisenberg Cosets
• Duality of subregular W-algebras and principal W-superalgebras
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• On resolution of highest weight modules over the $\mathcal{N}=2$ superconformal algebra