Logarithmic Conformal Field Theories

We analyse the SU(2) k WZNW models beyond the integrable representations and in particular the case of SU(2) 0. We find that these are good examples of logarithmic conformal field theories as indecomposable representations are naturally produced in the fusion of discrete irreducible representations. We also find extra, chiral and non-chiral, multiplet structure in the theory. The chiral fields, which we construct explicitly in SU(2) 0 , generate extended algebras within the model. We also study the process of quantum hamiltonian reduction of SU(2) 0 , giving the c = −2 triplet model, in both the free field approach and at the level of correlation functions. For rational level SU(2) k this gives us a useful technique to study the h 1,s correlators of the c p,q models and we find very similar structures to SU(2) 0. We also discuss LCFT as a limit of a sequence of ordinary CFTs and some of the subtleties that can occur. Acknowledgments I am very grateful for all the support and help I have received throughout my D.Phil. First and foremost I would like to thank my supervisor Dr Ian Kogan for his in-spirational insight, guidance and enthusiasm. I would also like to thank the many participants of the past two conferences in LCFT from whom I learnt a great deal. I am grateful to my office mates for many useful discussions and for tolerating my mess. I am also grateful to many others in the department who have provided a friendly and intellectually stimulating environment. A big thank you also to all my other friends and house-mates for making my time in Oxford so enjoyable. I am grateful to PPARC and Worcester College, Oxford for their financial support. Finally special thanks to all my family, and particularly my parents, for all their support.