VIRASORO ALGEBRAS WITH CENTRAL CHARGE c < 1

Bowcock, P.; Goddard, P.

Abstract

It is known that, given an algebra and a subalgebra, g ⊃ h, the difference of the Sugawara constructions of the Virasoro algebras associated with the corresponding Kac-Moody algebras ĝ ⊃ ĥ defines another Virasoro algebra, v̂, and also that if the central charge of c of v̂ is less than 1, ĝ is finitely reducible with respect to ĥ ⊕ v̂. The converse, that finite reducibility implies c < 1, is shown to hold. The construction is shown to lead to relationships between the modular transformation properties of characters of the Virasoro and Kac-Moody algebras and the relevance of this to the construction of modular invariants is discussed. A complete list of cases for which c < 1 is given.

• Presentation Conference Type: Conference Paper (published)
• Acceptance Date: Sep 26, 2002
• Online Publication Date: Oct 26, 2002
• Publication Date: 1987
• Journal: Nuclear Physics B
• Print ISSN: 0550-3213
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: B285
• Pages: 651-670
• DOI: https://doi.org/10.1016/0550-3213%2887%2990360-9
• Public URL: https://durham-repository.worktribe.com/output/1162107