Some aspects of c = ‐2 theory

Abstract

We investigate some aspects of the c = ‐2 logarithmic conformal field theory (LCFT). At first, we calculate some correlators of logarithmic conformal fields which have third order singular OPE with the energy‐momentum tensor. Then, we argue about the fields in the c = ‐2 model which are associated with this kind of more general logarithmic primary fields. We go on to find fermionic representations for all the fields in the extended Kac table, in particular the untwisted sector. Moreover, we calculate the various OPEs of the fields, especially for the logarithmic energy‐momentum tensor and by using these OPEs we find the exact finite transformation of this field. We briefly discuss about the important role of the zero modes in the c = ‐2 model. Finally we consider the perturbation of this theory and its relationship with integrable models, and generalization of Zamalodchikov's c‐theorem.