Non-unitary Minimal Models Research Articles

Fermionic sum representations for conformal field theory characters

We present sum representations for all characters of the unitary Virasoro minimal models. They can be viewed as fermionic companions of the Rocha-Caridi sum representations, the latter related to the (bosonic) Feigin-Fuchs-Felder construction. We also give fermionic representations for certain characters of the general ( G (1)) k × ( G (1)) l ( G (1)) k+l coset conformal field theories, the non-unitary minimal models M(p, p+2) and M(p, kp+1) , the N = 2 superconformal series, and the Z N -parafermion theories, and relate the q→1 behaviour of all these fermionic sum representations to the thermodynamic Bethe ansatz.

Exact resonance ADE S-matrices and their renormalization group trajectories

We introduce the ADE resonance factorized models as an appropriate analytical continuation of the Toda S-matrices to the complex values of their coupling constant. An investigation of the associated Casimir energy, via the thermodynamic Bethe ansatz, reveals a rich pattern of renormalization group trajectories interpolating between the central charges of the G 1⊗ G k G k+1 GKO coset models. We have also constructed the simplest resonance factorized model satisfying the “φ 3”-property. From this resonance scattering, we predict new flows in non-unitary minimal models.

Renormalization-group trajectories from resonance factorized S matrices.

We propose and investigate a large class of models possessing resonance factorized S matrices. The associated Casimir energy describes a rich pattern of renormalization-group trajectories related to flows in the coset models based on the simply laced Lie algebras. From a simple resonance S matrix satisfying the ``${\mathrm{\ensuremath{\varphi}}}^{3}$ property'' we predict new flows in nonunitary minimal models.

Scattering matrices for φ1,2 perturbed conformal minimal models in absence of kink states

We determine the spectrum and the factorizable S-matrices of the massive excitations of the non-unitary minimal models M 2,2n + 1 perturbed by the operator ø 1,2. These models present no kinks as asymptotic states, as follows from the reduction of the Zhiber-Mikhailov-Shabat model with respect to the quantum group SL(2) q found by Smirnov. We also give the whole set of S-matrices of the non-unitary minimal model M 2,9 perturbed by the operator ø 1,4, which is related to a RSOS reduction for the ø 1,2 operator of the unitary model M 8,9. The thermodynamical Bethe ansatz and the truncated conformal space approach are applied to these scattering theories in order to support their interpretation.

φ 1,2 deformation of the [formula omitted]2,2 n+1 conformal minimal models

The spectrum and the factorizable S-matrices of the massive excitations of the φ 1,2 deformation of the nonunitary minimal models M 2,2 n+1 is given. These models present no kinks as asymptotic states, as follows from the reduction of the Zhiber-Mikhailov-Shabat model with respect to the quantum group SL(2) q , found by Smirnov. An interesting situation of zeros and poles overlapping in the physical amplitudes is also discussed.

Scaling non-unitary models with degenerate ground state. Thermodynamic Bethe ansatz approach

We discuss a class of the non-unitary minimal models with degenerate ground state, namely the M 3/ q theories perturbed by the operator ø 1,3. We show that the thermodynamic Bethe ansatz approach can be also applied to the second lowest state in these systems. We compare our results with perturbation theory and with the truncated conformal space method.

Non-unitary minimal models and RSOS models

We study a class of RSOS models whose universal classes are the non-unitary minimal models of the W n algebra. The ground-state structure is investigated, and the parametrization the dominant integral weights of A n−1 (1) is given. Using it, the local-state probabilities are constructed in terms of the W n characters. This shows the scaling relations between the critical exponents of a non-unitary RSOS model and the anomalous dimensions of the primary fields of the corresponding minimal model.

The ising model coupled to 2D gravity. A nonperturbative analysis

We apply recently developed techniques to give an exact nonperturbative solution of the two matrix realization of the Ising model coupled to 2D lattice gravity. We demonstrate that the Ising model is different from multicritical matter. We conjecture that multicritical matter is described by certain non-unitary minimal models.

Quantum group structure in the unitary minimal model

We obtain a symmetry algebra for any unitary minimal model by using the representation of conformal field theories. This symmetry algebra can be interpreted as a quantum group. The generalization to non-unitary minimal models is direct.