A Note on Four-Point Functions in Logarithmic Conformal Field Theory

TL;DR

This paper analyzes the structure of four-point functions in logarithmic conformal field theory, providing an algorithm to handle indecomposable representations and reduce free parameters using permutation symmetries.

Contribution

It introduces a systematic algorithm for four-point functions in logarithmic CFT with indecomposable representations, enhancing understanding of their structure.

Findings

Derived the generic form of 4-point functions in logarithmic CFT.

Developed an algorithm to simplify the structure using permutation symmetries.

Illustrated the approach with non-trivial examples.

Abstract

The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The presented algorithm is illustrated with some non-trivial examples and permutation symmetries are exploited to reduce the number of free structure-functions, which cannot be fixed by global conformal invariance alone.