engleski

Embeddings of vertex operator algebras associated to orthogonal affine Lie algebras

Let $L_{; ; D_{; ; \ell}; ; }; ; (-\ell +\frac{; ; 3}; ; {; ; 2}; ; , 0)$ (resp. $L_{; ; B_{; ; \ell}; ; }; ; (-\ell +\frac{; ; 3}; ; {; ; 2}; ; , 0)$) 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 + \frac{; ; 3}; ; {; ; 2}; ; $. We show that $L_{; ; D_{; ; \ell}; ; }; ; (-\ell +\frac{; ; 3}; ; {; ; 2}; ; , 0)$ is a vertex subalgebra of $L_{; ; B_{; ; \ell}; ; }; ; (-\ell +\frac{; ; 3}; ; {; ; 2}; ; , 0)$ with the same conformal vector. For $\ell =4$, $L_{; ; D_{; ; 4}; ; }; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$ is a vertex subalgebra of three copies of $L_{; ; B_{; ; 4}; ; }; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$ contained in $L_{; ; F_{; ; 4}; ; }; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$, and all five of these vertex operator algebras have the same conformal vector.

vertex operator algebra; affine Kac-Moody algebra; conformal embedding

nije evidentirano