Conformal nets from minimal W-algebras

Abstract

We show the strong graded locality of all unitary minimal W-algebras, so that they give rise to irreducible graded-local conformal nets. Among these unitary vertex superalgebras, up to taking tensor products with free fermion vertex superalgebras, there are the unitary Virasoro vertex algebras (N=0) and the unitary N=1,2,3,4 super-Virasoro vertex superalgebras. Accordingly, we have a uniform construction that gives, besides the already known N=0,1,2 super-Virasoro nets, also the new N=3,4 super-Virasoro nets. All strongly rational unitary minimal W-algebras give rise to previously known completely rational graded-local conformal nets and we conjecture that the converse is also true. We prove this conjecture for all unitary W-algebras corresponding to the N=0,1,2,3,4 super-Virasoro vertex superalgebras.

39 pages, final author's version of the original article published in Communications in Mathematical Physics

References in corpus (31)

• Quantum Reduction for Affine Superalgebras
• Finite vs. affine W-algebras
• W-algebras as coset vertex algebras
• Conformal Subnets and Intermediate Subfactors
• Schur-Weyl Duality for Heisenberg Cosets
• Topological Sectors and a Dichotomy in Conformal Field Theory
• On the representation theory of Virasoro Nets
• Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural results
• Structure and Classification of Superconformal Nets
• Conformal Field Theory, Tensor Categories and Operator Algebras
• Modularity in orbifold theory for vertex operator superalgebras
• Conformal covariance and the split property
• Conformal Covariance and Positivity of Energy in Charged Sectors
• N=2 superconformal nets
• Haploid algebras in $C^{\ast }$-tensor categories and the Schellekens list
• The Virasoro algebra and sectors with infinite statistical dimension
• Q-systems and extensions of completely unitary vertex operator algebras
• The extensions of $L_{s{l}_2}(k,0)$ and preunitary vertex operator algebra with central charges $c<1$
• Fusion and positivity in chiral conformal field theory
• Unitary representations of the ${\mathcal{W}}_3$-algebra with $c\ge 2$
• Superconformal nets and noncommutative geometry
• Local equivalence of representations of Diff${}^{+}(S^1)$ corresponding to different highest weights
• Classification of unitary vertex subalgebras and conformal subnets for rank-one lattice chiral CFT models
• Wightman fields for two-dimensional conformal field theories with pointed representation category
• Unitarity of minimal $W$-algebras and their representations I
• Energy bounds for vertex operator algebra extensions
• Super-KMS functionals for graded-local conformal nets
• From vertex operator superalgebras to graded-local conformal nets and back
• Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24
• Non-unitary Wightman CFTs and non-unitary vertex algebras
• Unitarity of minimal $W$-algebras and their representations II: Ramond sector

Cited by in corpus (1)

• From vertex operator superalgebras to graded-local conformal nets and back