Related papers: Conformal nets from minimal W-algebras
Lie conformal algebras $\mathcal{W}(a,b)$ are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we give a complete classification of extensions of finite irreducible…
For every odd p \geq 3, we investigate representation theory of the vertex algebra WW_{2,p} associated to (2,p) minimal models for the Virasoro algebras. We demonstrate that vertex algebras WW_{2,p} are C_2--cofinite and irrational.…
We study the general structure of Fermi conformal nets of von Neumann algebras on the circle, consider a class of topological representations, the general representations, that we characterize as Neveu-Schwarz or Ramond representations, in…
For the affine vertex algebra $V_k(\mathfrak{g})$ at an admissible level $k$ of $\hat{\mathfrak{g}}$, we prove that certain subcategory of weak $V_k(\mathfrak{g})$-module category is semisimple. As a consequence, we show that…
We study the representation theory of the N=1 super Heisenberg-Virasoro vertex algebra at level zero, which extends the previous work on the Heisenberg-Virasoro vertex algebra arXiv:math/0201314, arXiv:1405.1707 and arXiv:1703.00531 to the…
We construct holomorphic local conformal framed nets extended from a tensor power of the Virasoro net with c=1/2 with a pair of binary codes (C,D) satisfying the conditions given by Lam and Yamauchi for holomorphic framed vertex operator…
The problem of the classification of the extensions of the Virasoro algebra is discussed. It is shown that all $H$-reduced $\hat{\cal G}_{r}$-current algebras belong to one of the following basic algebraic structures: local quadratic…
In this paper, we obtain a class of $\mathbb{Z}$-graded conformal algebras which is induced by Heisenberg-Virasoro conformal algebra. More precisely, we classify $\mathbb{Z}$-graded conformal algebras $\mathcal{A} =…
We construct infinite dimensional spectral triples associated with representations of the super-Virasoro algebra. In particular the irreducible, unitary positive energy representation of the Ramond algebra with central charge c and minimal…
We establish rigid tensor category structure on finitely-generated weight modules for the subregular $W$-algebras of $\mathfrak{sl}_n$ at levels $ - n + \frac{n}{n+1}$ (the $\mathcal{B}_{n+1}$-algebras of Creutzig-Ridout-Wood) and at levels…
We review the new approach to the theory of nonlinear $W$-algebras which is developed recently and called {\it conformal linearization}. In this approach $W$-algebras are embedded as subalgebras into some {\it linear conformal} algebras…
We demonstrate that all rational models of the N=2 super Virasoro algebra are unitary. Our arguments are based on three different methods: we determine Zhu's algebra (for which we give a physically motivated derivation) explicitly for…
We study local algebras, which are structures similar to $\mathbb{Z}$-graded algebras concentrated in degrees $-1,0,1$, but without a product defined for pairs of elements at the same degree $\pm1$. To any triple consisting of a Kac-Moody…
We investigate the representation theory of some recently constructed N=2 super W-algebras with two generators. Except for the central charges in the unitary minimal series of the N=2 super Virasoro algebra we find no new rational models.…
We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We…
SW(3/2,2) superconformal algebra is W algebra with two Virasoro operators. The Kac determinant is calculated and the complete list of unitary representations is determined. Two types of extensions of SW(3/2,2) algebra are discussed. A new…
In the present contribution, I report on certain {\it non-linear} and {\it non-local} extensions of the conformal (Virasoro) algebra. These so-called $V$-algebras are matrix generalizations of $W$-algebras. First, in the context of…
In this paper we study a class of modules over infinite-dimensional Lie (super)algebras, which we call conformal modules. In particular we classify and construct explicitly all irreducible conformal modules over the Virasoro and the N=1…
We prove that any unitary highest weight module over a universal minimal quantum affine $W$-algebra at non-critical level descends to its simple quotient. We find the defining relations of the unitary simple minimal quantum affine…
In a previous paper by the authors, we obtain the first example of a finitely freely generated simple $\mathbb Z$-graded Lie conformal algebra of linear growth that cannot be embedded into any general Lie conformal algebra. In this paper,…