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

TL;DR

This paper extends the mathematical framework of (1,p) logarithmic conformal field theories by introducing pseudocharacters, constructing a complete basis for torus amplitudes, and proposing boundary states satisfying the Cardy condition.

Contribution

It introduces pseudocharacters to complete the basis of torus amplitudes and proposes boundary states in (1,p) models that satisfy the Cardy condition.

Findings

Complete basis of torus amplitudes with pseudocharacters

Generalized Verlinde formula for structure constants

Construction of boundary states satisfying Cardy condition

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.