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Using GKO construction, we conjecture a formula for the characters of highest weight irreducible representations of the algebra of conformal models having S3 symmetry with spin 4/3 parafermionic currents constructed by Fateev and Zamolodchikov. The modular transformations of these characters are given and modular invariant partition functions are classified. It turns out that an A-D-E classification similar to that found in conformal and N=1 superconformal theories holds. For the particular case of the tricritical 3-state Potts model the connection with Virasoro characters is given.

The fact that in any rational conformal field theory (RCFT) four-point function on the sphere must satisfy an ordinary differential equation gives a simple condition on the conformal dimensions of primary fields. We discuss how this can help in the classification program of RCFT. As an example all associative fusion rules with less than four non-trivial primary fields and Nijk ⩽ 1 are discussed. Another application to the classification of chiral algebras is briefly mentioned.

We investigate boundary bound states of sine-Gordon model on the finite-size strip with Dirichlet boundary conditions. For the purpose we derive the nonlinear integral equation (NLIE) for the boundary excited states from the Bethe ansatz equation of the inhomogeneous XXZ spin 1/2 chain with boundary imaginary roots discovered by Saleur and Skorik. Taking a large volume (IR) limit we calculate boundary energies, boundary reflection factors and boundary Luscher corrections and compare with the excited boundary states of the Dirichlet sine-Gordon model first considered by Dorey and Mattsson. We also consider the short distance limit and relate the IR scattering data with that of the UV conformal field theory., Comment: LaTeX, 21 pages with 10 eps figures

By considering the continuum scaling limit of the $A_{4}$ RSOS lattice model of Andrews-Baxter-Forrester with integrable boundaries, we derive excited state TBA equations describing the boundary flows of the tricritical Ising model. Fixing the bulk weights to their critical values, the integrable boundary weights admit a parameter $\xi $ which plays the role of the perturbing boundary field $\phi_{1,3}$ and induces the renormalization group flow between boundary fixed points. The boundary TBA equations determining the RG flows are derived in the $\mathcal{B}_{(1,2)}\to \mathcal{B}_{(2,1)}$ example. The induced map between distinct Virasoro characters of the theory are specified in terms of distribution of zeros of the double row transfer matrix., Comment: Latex, 14 pages - Talk given at the Landau meeting "CFT and Integrable Models", Sept. 2002 - v2: some statements about $\phi_{1,2}$ perturbations corrected

In this letter we show that the R\'enyi entanglement entropy of a region of large size $\ell$ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as $S_n \sim \frac{c_{\mathrm{eff}}(n+1)}{6n} \log \ell$, where $c_{\mathrm{eff}}=c-24\Delta>0$ is the effective central charge, $c$ (which may be negative) is the central charge of the conformal field theory and $\Delta\neq 0$ is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic ($L_0 = \Delta I + N$ with $N$ nilpotent), then there is an additional term proportional to $\log(\log \ell)$. These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models., Comment: 5 pages, 2 figures. Revised version including new derivation of the EE of logarithmic CFT. To appear in J. Phys. A. (fast track communications)