The ABC (in any D) of Logarithmic CFT

TL;DR

This paper provides a comprehensive, model-independent analysis of the structure of logarithmic conformal field theories across all spacetime dimensions, focusing on correlation functions and conformal blocks, with applications to various physical models.

Contribution

It offers the first general form of correlation functions and conformal block decompositions for logarithmic CFTs, facilitating future bootstrap studies.

Findings

Derived the general form of correlation functions in logarithmic CFTs

Established conformal block decompositions for these theories

Discussed applications to models like percolation and holography

Abstract

Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our analysis is model-independent and holds for any spacetime dimension. Our results include a determination of the general form of correlation functions and conformal block decompositions, clearing the path for future bootstrap applications. Several examples are discussed in detail, including logarithmic generalized free fields, holographic models, self-avoiding random walks and critical percolation.