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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| Formato: | Artigo |
| Idioma: | English |
| Publicado em: |
Elsevier
2017-11-01
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| Colecção: | Nuclear Physics B |
| Acesso em linha: | http://www.sciencedirect.com/science/article/pii/S0550321317303188 |
| _version_ | 1830092146919604224 |
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| author | Olivier Blondeau-Fournier Pierre Mathieu Trevor A. Welsh |
| author_facet | Olivier Blondeau-Fournier Pierre Mathieu Trevor A. Welsh |
| author_sort | Olivier Blondeau-Fournier |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-16T17:32:35Z |
| format | Article |
| id | doaj.art-cf9d34778d5241a78e9ab4f94e7f4fd0 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-12-16T17:32:35Z |
| publishDate | 2017-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-cf9d34778d5241a78e9ab4f94e7f4fd02022-12-21T22:22:53ZengElsevierNuclear Physics B0550-32131873-15622017-11-01924C64368310.1016/j.nuclphysb.2017.09.023A quartet of fermionic expressions for M(k,2k±1) Virasoro characters via half-lattice pathsOlivier Blondeau-FournierPierre MathieuTrevor A. WelshWe 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.http://www.sciencedirect.com/science/article/pii/S0550321317303188 |
| spellingShingle | Olivier Blondeau-Fournier Pierre Mathieu Trevor A. Welsh A quartet of fermionic expressions for M(k,2k±1) Virasoro characters via half-lattice paths Nuclear Physics B |
| title | A quartet of fermionic expressions for M(k,2k±1) Virasoro characters via half-lattice paths |
| title_full | A quartet of fermionic expressions for M(k,2k±1) Virasoro characters via half-lattice paths |
| title_fullStr | A quartet of fermionic expressions for M(k,2k±1) Virasoro characters via half-lattice paths |
| title_full_unstemmed | A quartet of fermionic expressions for M(k,2k±1) Virasoro characters via half-lattice paths |
| title_short | A quartet of fermionic expressions for M(k,2k±1) Virasoro characters via half-lattice paths |
| title_sort | quartet of fermionic expressions for m k 2k 1 virasoro characters via half lattice paths |
| url | http://www.sciencedirect.com/science/article/pii/S0550321317303188 |
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