Global Conformal Invariance in D-dimensions and Logarithmic Correlation Functions

TL;DR

This paper explores the structure of logarithmic conformal field theories in D-dimensions, deriving correlation functions and demonstrating how they relate to ordinary conformal theories through differentiation.

Contribution

It introduces a formalism for transforming multiplets under the D-dimensional conformal group and calculates logarithmic two- and three-point functions, linking them to standard CFTs.

Findings

Derived explicit forms of logarithmic two- and three-point functions.

Showed how to obtain n-point functions of logarithmic theories from ordinary CFTs.

Established the transformation rules for multiplets under the conformal group.

Abstract

We define transformation of multiplets of fields (Jordan cells) under the D-dimensional conformal group, and calculate two and three point functions of fields, which show logarithmic behaviour. We also show how by a formal differentiation procedure, one can obtain n-point function of logarithmic field theory from those of ordinary conformal field theory.