On the relation between Φ ( 1 , 2 ) and Φ ( 1 , 5 ) perturbed minimal models and unitarity

We consider the RSOS S–matrices of the Φ(1,5) perturbed minimal models which have recently been found in the companion paper [1]. These S–matrices have some interesting properties, in particular, unitarity may be broken in a stronger sense than seen before, while one of the three classes of Φ(1,5) perturbations (to be described) shares the same Thermodynamic Bethe Ansatz as a related Φ(1,2) perturbation. We test these new S–matrices by the standard Truncated Conformal Space method, and further observe that in some cases the BA equations for two particle energy levels may be continued to complex rapidity to describe (a) single particle excitations and (b) complex eigenvalues of the Hamiltonian corresponding to non-unitary S–matrix elements. We make some comments on identities between characters in the two related models following from the fact that the two perturbed theories share the same breather sector. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]