Embedding of bases: from the \(\mathcal M(2,2\kappa+1)\) to the \(\mathcal M(3,4\kappa+2-\delta)\) models. (English) Zbl 1247.81426
Summary: A new quasi-particle basis of states is presented for all the irreducible modules of the \(M(3,p)\) models. It is formulated in terms of a combination of Virasoro modes and the modes of the field \(\varphi 2,1\). This leads to a fermionic expression for particular combinations of irreducible \(M(3,p)\) characters, which turns out to be identical with the previously known formula. Quite remarkably, this new quasi-particle basis embodies a sort of embedding, at the level of bases, of the minimal models \(M(2,2\kappa +1)\) into the \(M(3,4\kappa +2-\delta )\) ones, with \(0\leq \delta \leq 3\).
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
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