A quartet of fermionic expressions for M(k,2k±1) Virasoro characters via half-lattice paths
We derive new fermionic expressions for the characters of the Virasoro minimal models M(k,2k±1) by analysing the recently introduced half-lattice paths. These fermionic expressions display a quasiparticle formulation characteristic of the ϕ2,1 and ϕ1,5 integrable perturbations. We find that they ari...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2017-11-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321317303188 |
| Summary: | We derive new fermionic expressions for the characters of the Virasoro minimal models M(k,2k±1) by analysing the recently introduced half-lattice paths. These fermionic expressions display a quasiparticle formulation characteristic of the ϕ2,1 and ϕ1,5 integrable perturbations. We find that they arise by imposing a simple restriction on the RSOS quasiparticle states of the unitary models M(p,p+1). In fact, four fermionic expressions are obtained for each generating function of half-lattice paths of finite length L, and these lead to four distinct expressions for most characters χr,sk,2k±1. These are direct analogues of Melzer's expressions for M(p,p+1), and their proof entails revisiting, reworking and refining a proof of Melzer's identities which used combinatorial transforms on lattice paths.
We also derive a bosonic version of the generating functions of length L half-lattice paths, this expression being notable in that it involves q-trinomial coefficients. Taking the L→∞ limit shows that the generating functions for infinite length half-lattice paths are indeed the Virasoro characters χr,sk,2k±1. |
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| ISSN: | 0550-3213 1873-1562 |