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Solving the Ward Identities of Irrational Conformal Field Theory | | M.B. Halpern
; N.A. Obers
; | | Date: |
17 May 1993 | | Journal: | Int.J.Mod.Phys. A9 (1994) 419-460 | | Subject: | hep-th | | Abstract: | The affine-Virasoro Ward identities are a system of non-linear differential equations which describe the correlators of all affine-Virasoro constructions, including rational and irrational conformal field theory. We study the Ward identities in some detail, with several central results. First, we solve for the correlators of the affine-Sugawara nests, which are associated to the nested subgroups $gsupset h_1 supset ldots supset h_n$. We also find an equivalent algebraic formulation which allows us to find global solutions across the set of all affine-Virasoro constructions. A particular global solution is discussed which gives the correct nest correlators, exhibits braiding for all affine-Virasoro correlators, and shows good physical behavior, at least for four-point correlators at high level on simple $g$. In rational and irrational conformal field theory, the high-level fusion rules of the broken affine modules follow the Clebsch-Gordan coefficients of the representations. | | Source: | arXiv, hep-th/9305072 | | Services: | Forum | Review | PDF | Favorites | |
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