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

TL;DR

This paper presents a general method for constructing 3-point functions in conformal field theory with affine Lie group symmetry, using triangular coordinates and elementary polynomials, applicable to all simple Lie groups and representations.

Contribution

It introduces a novel framework for 3-point functions in affine Lie group symmetric CFTs, extending previous 2-point function work and providing a procedure for tensor product coefficient computation.

Findings

Method applicable to all simple Lie groups and representations

Explicit construction for SL(3), SL(4), and SO(5) cases

Simplifies couplings into products of elementary polynomials

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).