Recent Developments in Logarithmic Conformal Field Theory

by Flohr, Michael

Abstract

%% To be updated later %% We report on recent developments in the understanding and mathematical foundation of logarithmic conformal field theory. In particular, we disucss:\\ 1) The geometric origin of logarithmic operators for a certain class of logarithmic conformal field theories. The role of zero modes and the relation to deformations of the stress-energy tensor a la Fjelstad, Fuchs et al. are elucidated.\\ 2) The meaning of solutions of the modular differential equation, which cannot be understood as characters (i.e. traces over representation modules), is clarified, which leads to the necessity to generalize certain notions of rationality.