3-point Functions in Conformal Field Theory with Affine Lie Group Symmetry

Details 3-point Functions in Conformal Field Theory with Affine Lie Group Symmetry 3-point Functions in Conformal Field Theory with Affine Lie Group Symmetry

1998-07-20

arxiv.org/abs/hep-th/9807153v1

Int.J.Mod.Phys. A14 (1999) 1225-1260

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, LaTeX

Scientific paper

10.1142/S0217751X99000634

In this paper we develop a general method for constructing 3-point functions in conformal field theory with affine Lie group symmetry, continuing our recent work on 2-point functions. The results are provided in terms of triangular coordinates used in a wave function description of vectors in highest weight modules. In this framework, complicated couplings translate into ordinary products of certain elementary polynomials. The discussions pertain to all simple Lie groups and arbitrary integrable representation. An interesting by-product is a general procedure for computing tensor product coefficients, essentially by counting integer solutions to certain inequalities. As an illustration of the construction, we consider in great detail the three cases SL(3), SL(4) and SO(5).

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