The perturbations \(\phi_{2,1}\) and \(\phi_{1,5}\) of the minimal models \(M(p,p^\prime\)) and the trinomial analogue of Bailey’s lemma. (English) Zbl 0945.81057
Summary: We derive the fermionic polynomial generalizations of the characters of the integrable perturbations \(\phi_{2,1}\) and \(\phi_{1,5}\) of the general minimal \(M(p,p^\prime\)) conformal field theory by use of the recently discovered trinomial analogue of Bailey’s lemma. For \(\phi_{2,1}\) perturbations results are given for all models with \(2p>p^\prime\) and for \(\phi_{1,5}\) perturbations results for all models with \(p^\prime/3<p<p^\prime/2\) are obtained. For the \(\phi_{2,1}\) 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 \(\phi_{1,5}\) with \(2<p^\prime/p<5/2\) and for \(\phi_{2,1}\) satisfying \(3p<2p^\prime\) 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.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
Keywords:
integrable perturbations; minimal conformal field theory; trinomial analogue of Bailey’s lemmaReferences:
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