Unitary and non-unitary $N=2$ minimal models

Abstract

The unitary $N=2$ superconformal minimal models have a long history in string theory and mathematical physics, while their non-unitary (and logarithmic) cousins have recently attracted interest from mathematicians. Here, we give an efficient and uniform analysis of all these models as an application of a type of Schur-Weyl duality, as it pertains to the well-known Kazama-Suzuki coset construction. The results include straightforward classifications of the irreducible modules, branching rules, (super)characters and (Grothendieck) fusion rules.

arXiv comment32 pages

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Cited by in corpus (10)

• On fusion rules and intertwining operators for the Weyl vertex algebra
• A realisation of the Bershadsky--Polyakov algebras and their relaxed modules
• Braided Tensor Categories related to ${\mathcal{B}}_p$ Vertex Algebras
• Tensor structure on the Kazhdan-Lusztig category for affine $\mathfrak{gl}(1|1)$
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• $N=4$ superconformal algebras and diagonal cosets
• Fusion and (non)-rigidity of Virasoro Kac modules in logarithmic minimal models at $(p,q)$-central charge
• Staggered modules of $N=2$ superconformal minimal models
• Orthosymplectic Feigin-Semikhatov duality
• Fusion rules and rigidity for weight modules over the simple admissible affine $\mathfrak{sl}(2)$ and $\mathcal{N}=2$ superconformal vertex operator superalgebras