Level-rank duality via tensor categories

Abstract

We give a new way to derive branching rules for the conformal embedding $$(\asl_n)_m\oplus(\asl_m)_n\subset(\asl_{nm})_1.$$ In addition, we show that the category $\Cc(\asl_n)_m^0$ of degree zero integrable highest weight $(\asl_n)_m$-representations is braided equivalent to $\Cc(\asl_m)_n^0$ with the reversed braiding.

16 pages, to appear in Communications in Mathematical Physics. Version 2 changes: Proof of main theorem made explicit, example 4.11 removed, references updated

References in corpus (1)

• The rank-level duality for non-abelian theta functions

Cited by in corpus (11)

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• Fermionic Modular Categories and the 16-fold Way
• W-algebras as coset vertex algebras
• Tensor categories for vertex operator superalgebra extensions
• Braided tensor categories of admissible modules for affine Lie algebras
• Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• Cosets of free field algebras via arc spaces
• Invariant subalgebras of the small $\mathcal{N}=4$ superconformal algebra
• Feigin-Semikhatov conjecture and related topics
• Interpolation categories for Conformal Embeddings