Logarithmic Conformal Field Theory Through Nilpotent Conformal Dimensions

TL;DR

This paper introduces nilpotent conformal weights to analyze logarithmic conformal field theories, deriving their transformation laws, singular vectors, correlation functions, and discussing the emergence of a logarithmic partner to the energy momentum tensor.

Contribution

The paper presents a novel approach using nilpotent conformal weights to systematically study LCFTs and their unique features.

Findings

Derived transformation laws for LCFTs

Identified the structure of correlation functions in LCFTs

Discovered the emergence of an extra energy momentum tensor

Abstract

We study logarithmic conformal field theories (LCFTs) through the introduction of nilpotent conformal weights. Using this device, we derive the properties of LCFT's such as the transformation laws, singular vectors and the structure of correlation functions. We discuss the emergence of an extra energy momentum tensor, which is the logarithmic partner of the energy momentum tensor.