The perturbations φ2,1 and φ1,5 of the minimal models M(p, p′) and the trinomial analogue of Bailey's lemma

We derive the fermionic polynomial generalizations of the characters of the integrable perturbations φ2,1 and φ1,5 of the general minimal M(p, p′) conformal field theory by use of the recently discovered trinomial analogue of Bailey's lemma. For φ2,1 perturbations results are given for all models with 2p > p′ and for φ1,5 perturbations results for all models with p′/3 < p < p′/2 are obtained. For the φ2,1 perturbation of the unitary case M(p, p + 1) we use the incidence matrix obtained from these character polynomials to discuss possible TBA equations. We also find that for φ1,5 with 2 < p′/p < 52 and for φ2,1 satisfying p < 2p′ there are usually several different fermionic polynomials which lead to the identical bosonic polynomial. We interpret this to mean that in these cases the specification of the perturbing field is not sufficient to define the theory and that an independent statement of the choice of the proper vacuum must be made.