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

Abstract

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).

30 pages, LaTeX

References in corpus (3)

• Free Field Realizations of Affine Current Superalgebras, Screening Currents and Primary Fields
• Two-point Functions in Affine SL(N) Current Algebra
• Screening Currents in Affine Current Algebra

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• Fusion in coset CFT from admissible singular-vector decoupling
• N-point and higher-genus osp(1|2) fusion
• Higher-genus su(N) fusion multiplicities as polytope volumes
• Purely affine elementary su(N) fusions