From boundary to bulk in logarithmic CFT

The analogue of the charge-conjugation modular invariant for rational logarithmic conformal field theories is constructed. This is done by reconstructing the bulk spectrum from a simple boundary condition ( the analogue of the Cardy 'identity brane'). We apply the general method to the c(1,p) triplet models and reproduce the previously known bulk theory for p = 2 at c = -2. For general p we verify that the resulting partition functions are modular invariant. We also construct the complete set of 2p boundary states, and confirm that the identity brane from which we started indeed exists. As a by-product we obtain a logarithmic version of the Verlinde formula for the c(1,p) triplet models.