Radford, Drinfeld, and Cardy boundary states in (1,p) logarithmic conformal field models

Abstract

We introduce p-1 pseudocharacters in the space of (1,p) model vacuum torus amplitudes to complete the distinguished basis in the 2p-dimensional fusion algebra to a basis in the whole (3p-1)-dimensional space of torus amplitudes, and the structure constants in this basis are integer numbers. We obtain a generalized Verlinde-formula that gives these structure constants. In the context of theories with boundaries, we identify the space of vacuum torus amplitudes with the space of Ishibashi states. Then, we propose 3p-1 boundary states satisfying the Cardy condition.