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Related papers: Conformal nets from minimal W-algebras

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In this paper, we study Virasoro vertex algebras and affine vertex algebras over a general field of characteristic $p>2$. More specifically, we study certain quotients of the universal Virasoro and affine vertex algebras by ideals related…

Quantum Algebra · Mathematics 2017-11-07 Xiangyu Jiao , Haisheng Li , Qiang Mu

We study the representation theory of the superconformal algebra $W_k(g,f_{\theta})$ associated with a minimal gradation of $g$. Here, $g$ is a simple finite-dimensional Lie superalgebra with a non-degenerate, even supersymmetric invariant…

Mathematical Physics · Physics 2016-09-07 Tomoyuki Arakawa

We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by 'lowest weight vectors'. We show that such vertex algebras have a 'good' representation theory in the…

Quantum Algebra · Mathematics 2015-06-16 Rob Laber , Geoffrey Mason

We begin a systematic study of unitary representations of minimal $W$-algebras. In particular, we classify unitary minimal $W$-algebras and make substantial progress in classification of their unitary irreducible highest weight modules. We…

Representation Theory · Mathematics 2023-07-03 Victor G. Kac , Pierluigi Möseneder Frajria , Paolo Papi

We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m \geq 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p \geq 2$, important in logarithmic conformal field theory. We…

Quantum Algebra · Mathematics 2009-04-17 Drazen Adamovic , Antun Milas

We show that every unitary positive energy representation W of the Virasoro algebra exponentiates to a holomorphic *-representation of the semigroup of annuli by bounded operators on the Hilbert space completion of W. We use this to show…

Functional Analysis · Mathematics 2025-06-11 André G. Henriques , James E. Tener

We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) W_N(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten…

High Energy Physics - Theory · Physics 2015-05-18 Elaine Beltaos , Terry Gannon

We show that if every module W for a vertex operator algebra V satisfies the condition that the dimension of W/C_1(W) is less than infinity, where C_1(W) is the subspace of W spanned by elements of the form u_{-1}w for u in V of positive…

Quantum Algebra · Mathematics 2007-05-23 Yi-Zhi Huang

We explore new connections between the fields and local observables in two dimensional chiral conformal field theory. We show that in a broad class of examples, the von Neumann algebras of local observables (a conformal net) can be obtained…

Mathematical Physics · Physics 2019-04-24 James E. Tener

In this paper we consider extensions of the super Virasoro algebra by one and two super primary fields. Using a non-explicitly covariant approach we compute all SW-algebras with one generator of dimension up to 7 in addition to the super…

High Energy Physics - Theory · Physics 2015-02-03 R. Blumenhagen , W. Eholzer , A. Honecker , R. Huebel

In this paper, we classify the following simple $\mathbb{Z}$-graded Lie conformal algebras $\mathcal{L}=\bigoplus_{i\in \mathbb{Z}}\mathcal{L}_i$ such that (1)$rank\mathcal{L}_i\leq 1$, (2)$\mathcal{L}_0$ is the Virasoro Lie conformal…

Rings and Algebras · Mathematics 2025-03-12 Maosen Xu

In this paper we continue the study of representation theory of formal distribution Lie superalgebras initiated in q-alg/9706030. We study finite Verma-type conformal modules over the N=2, N=3 and the two N=4 superconformal algebras and…

Quantum Algebra · Mathematics 2009-10-31 Shun-Jen Cheng , Ngau Lam

In this paper the W-algebra W(2,2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to a highest irreducible…

Quantum Algebra · Mathematics 2007-11-30 W. Zhang , C. Dong

We present a new conformal algebra. It is Z2 x Z2 graded and generated by three N=1 superconformal algebras coupled to each other by nontrivial relations of parafermionic type. The representation theory and unitary models of the algebra are…

High Energy Physics - Theory · Physics 2009-01-23 Boris Noyvert

It is proved that an irreducible module over the non-graded Virasoro-like algebra, which satisfies a natural condition, is a GHW module or uniformly bounded. Furthermore, the classification of some uniformly bounded modules is given.

Representation Theory · Mathematics 2007-11-16 Shoulan Gao , Cuipo Jiang

A systematic construction of super W-algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by…

High Energy Physics - Theory · Physics 2015-06-26 L. A. Ferreira , J. F. Gomes , R. M. Ricotta , A. H. Zimerman

This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay the foundation for this study. For any vector space $W$,…

Quantum Algebra · Mathematics 2007-05-23 Haisheng Li

In this paper we discuss the structure of the tensor product V'_{\alpha,\beta}\otimes L(c,h) of irreducible module from intermediate series and irreducible highest weight module over the Virasoro algebra. We generalize Zhang's…

Representation Theory · Mathematics 2013-08-12 Gordan Radobolja

Prototypical rational vertex operator algebras are associated to affine Lie algebras at positive integer level k. They correspond physically to the Wess-Zumino-Witten theories, and their representation theory can be captured by quantum…

Quantum Algebra · Mathematics 2025-11-04 Terry Gannon

We obtain a complete classification of minimal simple unitary $W$-algebras.

Representation Theory · Mathematics 2024-08-05 Victor G. Kac , Pierluigi Möseneder Frajria , Paolo Papi