Fusion rules for the logarithmic $N=1$ superconformal minimal models II: including the Ramond sector

Abstract

The Virasoro logarithmic minimal models were intensively studied by several groups over the last ten years with much attention paid to the fusion rules and the structures of the indecomposable representations that fusion generates. The analogous study of the fusion rules of the $N=1$ superconformal logarithmic minimal models was initiated in arXiv:1504.03155 as a continuum counterpart to the lattice explorations of arXiv:1312.6763. These works restricted fusion considerations to Neveu-Schwarz representations. Here, this is extended to include the Ramond sector. Technical advances that make this possible include a fermionic Verlinde formula applicable to logarithmic conformal field theories and a twisted version of the fusion algorithm of Nahm and Gaberdiel-Kausch. The results include the first construction and detailed analysis of logarithmic structures in the Ramond sector.

42 pages, 7 figures; v2 fixed minor typos and added a little more explanatory material

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Cited by in corpus (10)

• Cosets, characters and fusion for admissible-level $\mathfrak{osp}(1|2)$ minimal models
• Modularity of logarithmic parafermion vertex algebras
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
• Unitary and non-unitary $N=2$ minimal models
• Admissible-level ${\mathfrak{sl}}_3$ minimal models
• Modularity of Bershadsky-Polyakov minimal models
• 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
• Staggered and affine Kac modules over $A_1^{(1)}$
• Fusion rules and rigidity for weight modules over the simple admissible affine $\mathfrak{sl}(2)$ and $\mathcal{N}=2$ superconformal vertex operator superalgebras