Some Aspects of c=-2 Theory

TL;DR

This paper explores the structure, representations, and algebraic features of the c=-2 logarithmic conformal field theory, including its fermionic representations, operator product expansions, and connections to integrable models and c-theorem generalizations.

Contribution

It provides a detailed analysis of the representations, algebraic structures, and perturbations of the c=-2 logarithmic conformal field theory, highlighting new insights into its fermionic sectors and zero mode roles.

Findings

Identified fermionic representations in the extended Kac table.

Calculated key operator product expansions, including the energy-momentum tensor.

Explored perturbations and their links to integrable models and c-theorem generalizations.

Abstract

We investigate some aspects of the c=-2 logarithmic conformal field theory. These include the various representations related to this theory, the structures which come out of the Zhu algebra and the W algebra related to this theory. We try to find the fermionic representations of all of the fields in the extended Kac table especially for the untwisted sector case. In addition, we calculate the various OPEs of the fields, especially the energy-momentum tensor. Moreover, we investigate the important role of the zero modes in this model. We close the paper by considering the perturbations of this theory and their relationship to integrable models and generalization of Zamolodchikov's $c-$theorem.