Embeddings of vertex operator algebras associated to orthogonal affine Lie algebras

Abstract

Let $L_{D_{\ell }}(-\ell +3/2,0)$ (resp. $L_{B_{\ell }}(-\ell +3/2,0)$) be the simple vertex operator algebra associated to affine Lie algebra of type $D_{\ell }^{(1)}$ (resp. $B_{\ell }^{(1)}$) with the lowest admissible half-integer level $-\ell +3/2$. We show that $L_{D_{\ell }}(-\ell +3/2,0)$ is a vertex subalgebra of $L_{B_{\ell }}(-\ell +3/2,0)$ with the same conformal vector. For $\ell =4$, $L_{D_4}(-5/2,0)$ is a vertex subalgebra of three copies of $L_{B_4}(-5/2,0)$ contained in $L_{F_4}(-5/2,0)$, and all five of these vertex operator algebras have the same conformal vector.

arXiv comment21 pages, LaTeX; revised version

References in corpus (1)

• Vertex Algebras and Algebraic Curves