Energy bounds for vertex operator algebra extensions

Abstract

Let V be a simple unitary vertex operator algebra and U be a (polynomially) energy-bounded unitary subalgebra containing the conformal vector of V. We give two sufficient conditions implying that V is energy-bounded. The first condition is that U is a compact orbifold for some compact group G of unitary automorphisms of V. The second condition is that V is exponentially energy-bounded and it is a finite direct sum of simple U-modules. As consequence of the second condition, we prove that if U is a regular energy-bounded unitary subalgebra of a simple unitary vertex operator V, then $V$ is energy-bounded. In particular, every simple unitary extension (with the same conformal vector) of a simple unitary affine vertex operator algebra associated with a semisimple Lie algebra is energy-bounded.

arXiv comment19 pages, revised version

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Cited by in corpus (5)

• Haploid algebras in $C^{\ast }$-tensor categories and the Schellekens list
• From vertex operator superalgebras to graded-local conformal nets and back
• Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24
• Geometric Positivity of the Fusion Products of Unitary Vertex Operator Algebra Modules
• Conformal nets from minimal W-algebras