On Modular Invariant Partition Functions of Conformal Field Theories with Logarithmic Operators

TL;DR

This paper extends the concept of characters and partition functions to logarithmic conformal field theories, providing a classification similar to rational theories and exploring their modular invariance properties.

Contribution

It introduces a generalized framework for characters and partition functions in logarithmic CFTs and classifies theories with specific central charges akin to rational models.

Findings

Extended definitions of characters and partition functions for logarithmic CFTs

Established a classification of theories with c = c(p,1) similar to A-D-E classification

Demonstrated modular invariance properties in these extended theories

Abstract

We extend the definitions of characters and partition functions to the case of conformal field theories which contain operators with logarithmic correlation functions. As an example we consider the theories with central charge c = c(p,1) = 13-6(p+1/p), the ``border'' of the discrete minimal series. We show that there is a slightly generalized form of the property of rationality for such logarithmic theories. In particular, we obtain a classification of theories with c = c(p,1) which is similar to the A-D-E classification of c = 1 models.