Quasi root systems and vertex operator realizations of the Virasoro algebra

Details Quasi root systems and vertex operator realizations of the Virasoro algebra Quasi root systems and vertex operator realizations of the Virasoro algebra

2009-12-03

arxiv.org/abs/0912.0557v1

Physics

Mathematical Physics

44 pages

Scientific paper

A construction of the Virasoro algebra in terms of free massless two-dimensional boson fields is studied. The ansatz for the Virasoro field contains the most general unitary scaling dimension 2 expression built from vertex operators. The ansatz leads in a natural way to a concept of a quasi root system. This is a new notion generalizing the notion of a root system in the theory of Lie algebras. We introduce a definition of a quasi root system and provide an extensive list of examples. Explicit solutions of the ansatz are presented for a range of quasi root systems.

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