Cosets of the $\mathcal{W}^k(\mathfrak{sl}_4, f_{\text{subreg}})$-algebra

  title={Cosets of the \$\mathcal\{W\}^k(\mathfrak\{sl\}\_4, f\_\{\text\{subreg\}\})\$-algebra},
  author={Thomas Creutzig and Andrew R. Linshaw},
  journal={arXiv: Representation Theory},
Let $\mathcal {W}^k(\mathfrak{sl}_4, f_{\text {subreg}})$ be the universal $\mathcal{W}$-algebra associated to $\mathfrak{sl}_4$ with its subregular nilpotent element, and let $\mathcal {W}_k(\mathfrak{sl}_4, f_{\text {subreg}})$ be its simple quotient. There is a Heisenberg subalgebra $\mathcal{H}$, and we denote by $\mathcal{C}^k$ the coset $\text{Com}(\mathcal{H}, \mathcal {W}^k(\mathfrak{sl}_4, f_{\text {subreg}}))$, and by $\mathcal{C}_k$ its simple quotient. We show that for $k=-4+(m+4)/3… Expand
7 Citations
Universal two-parameter $\mathcal{W}_{\infty}$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots, N)$
We prove the longstanding physics conjecture that there exists a unique two-parameter $\mathcal{W}_{\infty}$-algebra which is freely generated of type $\mathcal{W}(2,3,\dots)$, and generated by theExpand
Universal two-parameter even spin W∞-algebra
Abstract We construct the unique two-parameter vertex algebra which is freely generated of type W ( 2 , 4 , 6 , … ) , and generated by the weights 2 and 4 fields. Subject to some mild constraints,Expand
Let V be a simple vertex operator algebra containing a rank n Heisenberg vertex algebra H and let C = Com(H;V) be the coset of H in V. Assuming that the module categories of interest are vertexExpand
Simple current extensions beyond semi-simplicity
Let [Formula: see text] be a simple vertex operator algebra (VOA) and consider a representation category of [Formula: see text] that is a vertex tensor category in the sense of Huang–Lepowsky. InExpand
Fusion categories for affine vertex algebras at admissible levels
The main result is that the category of ordinary modules of an affine vertex operator algebra of a simply laced Lie algebra at admissible level is rigid and thus a braided fusion category. If theExpand
Simple Current Extensions of Tensor Products of Vertex Operator Algebras
We study simple current extensions of tensor products of two vertex operator algebras satisfying certain conditions. We establish the relationship between the fusion rule for the simple currentExpand
Duality of subregular W-algebras and principal W-superalgebras
We prove Feigin-Frenkel type dualities between subregular W-algebras of type A, B and principal W-superalgebras of type $\mathfrak{sl}(1|n), \mathfrak{osp}(2|2n)$. The type A case proves a conjectureExpand


Cosets of Bershadsky–Polyakov algebras and rational $${\mathcal W}$$W-algebras of type A
The Bershadsky–Polyakov algebra is the $${\mathcal W}$$W-algebra associated to $${\mathfrak s}{\mathfrak l}_3$$sl3 with its minimal nilpotent element $$f_{\theta }$$fθ. For notational convenience weExpand
Orbifolds and Cosets of Minimal $${\mathcal{W}}$$W-Algebras
Let $${\mathfrak{g}}$$g be a simple, finite-dimensional Lie (super)algebra equipped with an embedding of $${\mathfrak{s}\mathfrak{l}_2}$$sl2 inducing the minimal gradation on $${\mathfrak{g}}$$g. TheExpand
The Structure of the Kac–Wang–Yan Algebra
The Lie algebra $${\mathcal{D}}$$D of regular differential operators on the circle has a universal central extension $${\hat{\mathcal{D}}}$$D^. The invariant subalgebra $${\hat{\mathcal{D}}^+}$$D^+Expand
A Hilbert theorem for vertex algebras
Given a simple vertex algebra $$ \mathcal{A} $$ and a reductive group G of automorphisms of $$ \mathcal{A} $$, the invariant subalgebra $$ {\mathcal{A}^G} $$ is strongly finitely generated in mostExpand
W-algebras for Argyres–Douglas theories
The Schur index of the $$(A_1, X_n)$$(A1,Xn)-Argyres–Douglas theory is conjecturally a character of a vertex operator algebra. Here such vertex algebras are found for the $$A_{\text {odd}}$$Aodd andExpand
Invariant theory and the $\mathcal{W}_{1+\infty}$ algebra with negative integral central charge
The vertex algebra W_{1+\infty,c} with central charge c may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integerExpand
Coset Constructions of Logarithmic (1, p) Models
One of the best understood families of logarithmic onformal field theories consists of the (1, p) models (p =  2, 3, . . .) of central charge c1, p=1 − 6(p − 1)2/p. This family includes the theoriesExpand
Vertex Algebras for S-duality
We define new deformable families of vertex operator algebras $\mathfrak{A}[\mathfrak{g}, \Psi, \sigma]$ associated to a large set of S-duality operations in four-dimensional supersymmetric gaugeExpand
Tensor categories for vertex operator superalgebra extensions
Let $V$ be a vertex operator algebra with a category $\mathcal{C}$ of (generalized) modules that has vertex tensor category structure, and thus braided tensor category structure, and let $A$ be aExpand
$ \mathcal{N}=1 $ supersymmetric higher spin holography on AdS3
A bstractWe propose a duality between a higher spin $ \mathcal{N}=1 $ supergravity on AdS3 and a large N limit of a family of $ \mathcal{N}=\left( {1,1} \right) $ superconformal field theories. TheExpand