Bethe ansatz for deformed WA N − 1 conformal field theories

We propose and investigate the thermodynamic Bethe ansatz equations for the minimal W p models (associated with the AN−1 Lie algebra) perturbed by the least (ZN invariant) primary field ΦN . Our results reproduce the expected ultraviolet and infrared regimes. In particular for the positive sign of the perturbation our equations describe the behaviour of the ground state flowing from the W p model to the next W p−1 fixed point. October 1991, Phys.Lett.B, in press on leave from Departamento de Fisica, Universidade Federal de S.Carlos, C.P. 676 S.Carlos 13560, Brazil [email protected] Recently Al.Zamolodchikov has pointed out the importance of the thermodynamic Bethe ansatz (TBA) in the context of the non-diagonal scattering theories [1,2]. In particular, for the RSOS models, the respective TBA equations for the ground state reproduce the expected ultraviolet and infrared behaviours. The RSOS scattering theory describe [1,3] the scaling behaviour of the minimal conformal Mp field theories perturbed by the φ1,3 operator. For the negative sign of the perturbation, the TBA equations describe the massive behaviour of the (p-1) Z2 symmetric kinks. On the other hand, for the positive sign, they describe the Renormalization Group (RG) trajectory flowing from the Mp critical point to the Mp−1 fixed point. This is a well known example of RG flow between two nontrivial fixed points [4,5]. It seems important to generalize this approach to other systems possessing “higher” symmetries. The natural candidates are the ZN -invariant conformal field theories related to the minimal W p models [6] with central charge c = (N −1)(1− N(N+1) p(p+1) ), p = N +1, N +2, ... . The analogue of the φ1,3 operator in the W N p theories is the least (ZN invariant) relevant primary field ΦN associated with the weight of the adjoint representation of SU(N)p+1−N , which has conformal dimension ∆ΦN = 1− N p+1 . For the sake of simplicity we first consider the W 3 p theory. The perturbed action is defined by AW 3 p = ACFT + λ ∫