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Vertex Algebras, Lie Algebras and Superstrings

Nils R. Scheithauer
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Abstract

Certain vertex algebras and Lie algebras arising in superstring theory are investigated. We show that the Fock space of a compactified Neveu-Schwarz superstring, i.e. a Neveu-Schwarz superstring moving on a torus, carries the structure of a vertex superalgebra with a Neveu-Schwarz element. This implies that the physical states of such a string form a Lie algebra. The same is true for the GSO-projected states. The structure of these Lie algebras is investigated in detail. In particular there is a natural invariant form on them. In case that the torus has Lorentzian signature the quotient of these Lie algebras by the kernel of this form is a generalized Kac-Moody algebra. The roots can be easily described. If the dimension of space-time is smaller than or equal to 10 we can even determine their multiplicities.

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Nils R. Scheithauer. 1998-02-09. Vertex Algebras, Lie Algebras and Superstrings. https://arxiv.org/abs/hep-th/9802058

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