2019/10/02 by Thomas Creutzig, Boris Feigin, Andrew R. Linshaw +1
Decision Sciences · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Connection (principal bundle) #Coset #Degenerate energy levels #Diagonal #Fuzzy and Soft Set Theory #Quotient #Vertex (graph theory) #Vertex operator algebra #hep-th #math.QA #math.RT
paper · pdf · doi:10.1093/imrn/rnaa078
published as Int. Math. Res. Not. 24 (2021), 18768-18811 · 34 pages
arxiv created 2019/10/02 · openalex created_date 2019/10/10 · openalex publication_date 2020/03/19 · arxiv updated 2022/03/07 · openalex updated_date 2026/08/05
Coset constructions of W-algebras have many applications, and were recently given for principal W-algebras of A, D, and E types by Arakawa together with the first and third authors. In this paper, we give coset constructions of the large and small N=4 superconformal algebras, which are the minimal W-algebras of \mathfrakd(2,1;a) and \mathfrakpsl(2|2), respectively. From these realizations, one finds a remarkable connection between the large N=4 algebra and the diagonal coset Ck1, k2 = Com(Vk1+k2(\mathfraksl2), Vk1(\mathfraksl2) ⊗ Vk2(\mathfraksl2)), namely, as two-parameter vertex algebras, Ck1, k2 coincides with the coset of the large N=4 algebra by its affine subalgebra. We also show that at special points in the parameter space, the simple quotients of these cosets are isomorphic to various W-algebras. As a corollary, we give new examples of strongly rational principal W-algebras of type C at degenerate admissible levels.