THE PERTURBATIONS PHI(2,1) AND PHI(1,5) OF THE MINIMAL MODELS M(P,P')AND THE TRINOMIAL ANALOG OF BAILEYS LEMMA

We derive the fermionic polynomial generalizations of the characters o f the integrable perturbations phi(2,1) and phi(1,5) of the general mi nimal M(p,p') conformal field theory by use of the recently discovered trinomial analogue of Bailey's lemma, For phi(2,1) perturbations resu lts are given for all models with 2p > p' and for phi(1,5) perturbatio ns results for all models with p'/3 < p < p'/2 are obtained. For the p hi(2,1) perturbation of the unitary case M(p, p + 1) we use the incide nce matrix obtained from these character polynomials to discuss possib le TEA equations. We also find that for phi(1,5) with 2 < p'/p < 5/2 a nd for phi(2,1) satisfying 3p < 2p' there are usually several differen t fermionic polynomials which lead to the identical bosonic polynomial . We interpret this to mean that in these cases the specification of t he perturbing field is not sufficient to define the theory and that an independent statement of the choice of the proper vacuum must be made . (C) 1998 Published by Elsevier Science B.V.