Factorized combinations of Virasoro characters (Q1970904)

In the beginning, the factorized form of a single Virasoro character on the base of the Gauss-Jacobi and Watson identities (1987, Capelli, Itzykson, Zuber; 1991, Christe; 1994, Kellendonk, Rösgen, Varnhagen; 1996, Eholzer, Skoruppa; 1998, Bytsko, Fring) is obtained by exploiting the quasiclassical asymptotics (in the limit \(q\to 1^-\)) of the usual sum representation. This method is then applied to the factorization of linear combination of characters for two minimal Virasoro models, resulting in a product of several basic blocks; the related explicit formulae are found. In particular, the secondary effective charge is introduced. It is proved rigorously that no other differences of two Virasoro characters are factorizable in the presented form. A set of new identities between different characters (including the generalized Rogers-Ramanujan identities) is derived. In conclusion, some possible physical applications of the obtained results are briefly discussed.