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Energy bounds condition for intertwining operators of type $B$, $C$, and $G_2$ unitary affine vertex operator algebras
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abstract
The energy bounds condition for intertwining operators of unitary rational vertex operator algebras (VOAs) was studied, first by A.Wassermann for type $A$ affine VOAs, and later by T.Loke for $c<1$ Virasoro VOAs, and by V.Toledano-Laredo for type $D$ affine VOAs. In this paper, we extend their results to affine VOAs of type $B$, $C$, and $G_2$. As a consequence, the modular tensor categories of these unitary vertex operator algebras are unitary.
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Rational and non-rational two-dimensional conformal field theories arising from lattices
Even lattices in an indefinite bilinear form classify two-dimensional conformal net extensions of Heisenberg nets under a discreteness assumption, with explicit rational and non-rational examples.
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