Logarithmic operators and logarithmic conformal field theories

TL;DR

This paper reviews logarithmic operators and conformal field theories, highlighting their significance in critical phenomena like percolation and random walks, and discusses the challenges in classifying these theories.

Contribution

It provides a comprehensive review of logarithmic conformal field theories, focusing on key examples such as c=-2 and c=0, and discusses their applications and classification issues.

Findings

c=0 theories describe critical points in random systems

Logarithmic CFTs are crucial for understanding certain 2D critical phenomena

Classification of logarithmic CFTs remains incomplete

Abstract

Logarithmic operators and logarithmic conformal field theories are reviewed. Prominent examples considered here include c=-2 and c=0 logarithmic conformal field theories. c=0 logarithmic conformal field theories are especially interesting since they describe some of the critical points of a variety of longstanding problems involving a two dimensional quantum particle moving in a spatially random potential, as well as critical two dimensional self avoiding random walks and percolation. Lack of classification of logarithmic conformal field theories remains a major impediment to progress towards finding complete solutions to these problems.