On logarithmic solutions to the conformal Ward identities

TL;DR

This paper provides a comprehensive analysis of the conformal Ward identities within logarithmic conformal field theory, deriving complete solutions for correlation functions without simplifying assumptions, and revealing hierarchical structures in the correlators.

Contribution

It offers the first general solution framework for conformal Ward identities in logarithmic CFT with rank-two Jordan cells, extending previous results without restrictive assumptions.

Findings

Correlators exhibit hierarchical structures similar to known cases.

Complete solutions for two- and three-point functions are derived.

Results extend existing literature on logarithmic conformal field theories.

Abstract

A general discussion of the conformal Ward identities is presented in the context of logarithmic conformal field theory with conformal Jordan cells of rank two. The logarithmic fields are taken to be quasi-primary. No simplifying assumptions are made about the operator-product expansions of the primary or logarithmic fields. Based on a very natural and general ansatz about the form of the two- and three-point functions, their complete solutions are worked out. The results are in accordance with and extend the known results. It is demonstrated, for example, that the correlators exhibit hierarchical structures similar to the ones found in the literature pertaining to certain simplifying assumptions.