Four-Point Functions in Logarithmic Conformal Field Theories

TL;DR

This paper analyzes four-point correlation functions in logarithmic conformal field theories, providing explicit results for Jordan-rank 2 and 3, and discussing the structure and degrees of freedom of these correlators.

Contribution

It introduces an algorithm for computing four-point functions in logarithmic CFTs and presents explicit results for Jordan-rank 2 and 3, including graphical representations.

Findings

Explicit four-point functions for Jordan-rank 2 and 3

Discussion of degrees of freedom in correlators

Results for two-logarithmic fields of arbitrary Jordan-rank

Abstract

The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The used algorithm is described and we present all results for Jordan-rank $r=2$ and $r=3$ where we make use of permutation symmetry and use a graphical representation for the results. A number of remaining degrees of freedom which can show up in the correlator are discussed in detail. Finally we present the results for two-logarithmic fields for arbitrary Jordan-rank.