An affine string vertex operator construction at an arbitrary level

Journal Article · Mon Sep 01 04:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532135· OSTI ID:538439

Gebert, R W ^[1]; Nicolai, H ^[2]

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1. Institute for Advanced Study, School of Natural Sciences, Princeton, New Jersey 08540 (United States)
2. Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Schlaatzweg 1, D-14473 Potsdam (Germany)

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{endash}Di Vecchia{endash}Fubini (DFF) {open_quotes}oscillators{close_quotes} 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{endash}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{endash}Moody algebras. A novel interpretation of the affine Weyl group as the {open_quotes}dimensional null reduction{close_quotes} of the corresponding hyperbolic Weyl group is given, which follows upon re-expression of the affine Weyl translations as Lorentz boosts. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 538439
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 9 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGEBRA
CHIRAL SYMMETRY
COMPACTIFICATION
LATTICE FIELD THEORY
LORENTZ TRANSFORMATIONS
OSCILLATORS
QUANTUM OPERATORS
STRING MODELS
VERTEX FUNCTIONS