Fusion rules for the logarithmic $N=1$ superconformal minimal models I: the Neveu-Schwarz sector

Abstract

It is now well known that non-local observables in critical statistical lattice models, polymers and percolation for example, may be modelled in the continuum scaling limit by logarithmic conformal field theories. Fusion rules for such theories, sometimes referred to as logarithmic minimal models, have been intensively studied over the last ten years in order to explore the representation-theoretic structures relevant to non-local observables. Motivated by recent lattice conjectures, this work studies the fusion rules of the $N=1$ supersymmetric analogues of these logarithmic minimal models in the Neveu-Schwarz sector. Fusion rules involving Ramond representations will be addressed in a sequel.

37 pages, 6 figures, v2 added clarifying remarks

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Cited by in corpus (10)

• Boundary algebras and Kac modules for logarithmic minimal models
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
• Modularity of logarithmic parafermion vertex algebras
• Fusion rules for the logarithmic $N=1$ superconformal minimal models II: including the Ramond sector
• Admissible-level ${\mathfrak{sl}}_3$ minimal models
• Modularity of Bershadsky-Polyakov minimal models
• Representations of the Nappi--Witten vertex operator algebra
• 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
• Fusion rules and rigidity for weight modules over the simple admissible affine $\mathfrak{sl}(2)$ and $\mathcal{N}=2$ superconformal vertex operator superalgebras