Virasoro algebras and coset space models
This article is an extension of a previous one [\textit{P. Goddard} and \textit{D. Olive}, Nucl. Phys. B 257, No.2, 226-252 (1985; see the preceding review Zbl 0661.17014)] in which the authors have used the affine Kac- Moody algebras to construct representations of the Virasoro algebra. By considering the coset spaces by dividing out a subalgebra \({\mathfrak h}\) of \({\mathfrak g}\), where \({\mathfrak g}\) is the Lie algebra on which the Kac-Moody algebra is modelled, one obtains again the Virasoro algebra but with different central charge. Furthermore, representations of the Kac-Moody algebra on positive-definite Hilbert spaces obeying a unitarity property automatically yield in this way unitary representations of the Virasoro algebra. In particular, choosing for the coset the quaternionic projective space \({\mathbb{H}}P^{n-1}\), a connection is found with the results of \textit{D. Friedan}, \textit{Z. Qiu} and \textit{S. Shenker} [Vertex operators in mathematics and physics, Publ., Math. Sci. Res. Inst. 3, 419-449 (1985; Zbl 0559.58010)]. The representations thus constructed can be made explicit by using the ``quark model'' picture, realizing the Kac- Moody generators in terms of Fermi fields arising from a realization of either the Neveu-Schwarz or Ramond algebra. Similar constructions in the case of supersymmetry are mentioned.
scientific article; zbMATH DE number 4079697