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  An affine string vertex operator construction at an arbitrary level

Gebert, R. W., & Nicolai, H. (1997). An affine string vertex operator construction at an arbitrary level. Journal of Mathematical Physics, 38(9), 4435-4450. doi:10.1063/1.532135.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5A82-5 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5A83-3
Genre: Journal Article

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328671.pdf (Publisher version), 209KB
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 Creators:
Gebert, Reinhold W.1, Author
Nicolai, Hermann2, Author              
Affiliations:
1External Organizations, ou_persistent13              
2Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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 Abstract: An affine vertex operator construction at an arbitrary level is presented which is based on a completely compactified chiral bosonic string whose momentum lattice is taken to be the (Minkowskian) affine weight lattice. This construction is manifestly physical in the sense of string theory, i.e., the vertex operators are functions of Del Giudice–Di Vecchia–Fubini (DFF) "oscillators" and the Lorentz generators, both of which commute with the Virasoro constraints. We therefore obtain explicit representations of affine highest weight modules in terms of physical (DDF) string states. This opens new perspectives on the representation theory of affine Kac–Moody algebras, especially in view of the simultaneous treatment of infinitely many affine highest weight representations of arbitrary level within a single state space as required for the study of hyperbolic Kac–Moody algebras. A novel interpretation of the affine Weyl group as the "dimensional null reduction" of the corresponding hyperbolic Weyl group is given, which follows upon re-expression of the affine Weyl translations as Lorentz boosts.

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Language(s): eng - English
 Dates: 1997-09
 Publication Status: Published in print
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 Identifiers: eDoc: 328671
ISI: A1997XW13200003
DOI: 10.1063/1.532135
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Title: Journal of Mathematical Physics
  Alternative Title : J. Math. Phys.
Source Genre: Journal
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Pages: - Volume / Issue: 38 (9) Sequence Number: - Start / End Page: 4435 - 4450 Identifier: ISSN: 0022-2488