Logarithmic Operators in Conformal Field Theory

TL;DR

This paper explores conformal field theories with logarithmic singularities, revealing that such singularities necessitate additional operators forming Jordan cells with primary operators, and provides an example of such a theory.

Contribution

It demonstrates the connection between logarithmic singularities and the structure of Jordan cells in conformal field theories, introducing new operators and an explicit example.

Findings

Logarithmic singularities imply additional operators in the theory.

These operators form Jordan cells with primary operators.

An explicit example of a conformal field theory with such features is provided.

Abstract

Conformal field theories with correlation functions which have logarithmic singularities are considered. It is shown that those singularities imply the existence of additional operators in the theory which together with ordinary primary operators form the basis of the Jordan cell for the operator $L_{0}$. An example of the field theory possessing such correlation functions is given.