Realizations of simple affine vertex algebras and their modules: the cases $\widehat{sl(2)}$ and $\widehat{osp(1,2)}$

Abstract

We study embeddings of the simple admissible affine vertex algebras $V_k(sl(2))$ and $V_k(osp(1,2))$, $k\notin {\mathbb{Z}}_{\ge 0}$, into the tensor product of rational Virasoro and $N=1$ Neveu-Schwarz vertex algebra with lattice vertex algebras. We prove that the admissible affine vertex algebra $V_k(sl(2))$ can be embedded into vertex algebra $L^{Vir}(c_{p,p^{\prime }},0)\otimes \Pi (0)$ where $L^{Vir}(c_{p,p^{\prime }},0)$ is suitable minimal Virasoro vertex algebra and $\Pi (0)$ is a vertex algebra of lattice type. By using these realizations we construct a family of weight, logarithmic and Whittaker $\widehat{sl(2)}$ and $\widehat{osp(1,2)}$--modules. As an application, we construct all irreducible degenerate Whittaker modules for $V_k(sl(2))$.

44 pages, to appear in Comm. Math. Phys

References in corpus (7)

• Lectures on Wakimoto modules, opers and the center at the critical level
• Fusion in Fractional Level sl^(2)-Theories with k=-1/2
• The N=1 triplet vertex operator superalgebras
• Relaxed highest-weight modules I: rank $1$ cases
• The N = 1 Triplet Vertex Operator Superalgebras: Twisted Sector
• From Jack polynomials to minimal model spectra
• A note on the affine vertex algebra associated to $\mathfrak{gl}(1|1)$ at the critical level and its generalizations

Cited by in corpus (6)

• Relaxed highest-weight modules I: rank $1$ cases
• Modularity of Bershadsky-Polyakov minimal models
• Subregular W-algebras of type A
• On resolution of highest weight modules over the $\mathcal{N}=2$ superconformal algebra
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras
• Staggered modules of $N=2$ superconformal minimal models