Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States
We generalize the results of [Comm. Math. Phys. 299 (2010), 825-866] (hidden Grassmann structure IV) to the case of excited states of the transfer matrix of the six-vertex model acting in the so-called Matsubara direction. We establish an equivalence between a scaling limit of the partition function...
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| Дата: | 2011 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146787 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States / H. Boos // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1467872025-02-23T19:52:59Z Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States Boos, H. We generalize the results of [Comm. Math. Phys. 299 (2010), 825-866] (hidden Grassmann structure IV) to the case of excited states of the transfer matrix of the six-vertex model acting in the so-called Matsubara direction. We establish an equivalence between a scaling limit of the partition function of the six-vertex model on a cylinder with quasi-local operators inserted and special boundary conditions, corresponding to particle-hole excitations, on the one hand, and certain three-point correlation functions of conformal field theory (CFT) on the other hand. As in hidden Grassmann structure IV, the fermionic basis developed in previous papers and its conformal limit are used for a description of the quasi-local operators. In paper IV we claimed that in the conformal limit the fermionic creation operators generate a basis equivalent to the basis of the descendant states in the conformal field theory modulo integrals of motion suggested by A. Zamolodchikov (1987). Here we argue that, in order to completely determine the transformation between the above fermionic basis and the basis of descendants in the CFT, we need to involve excitations. On the side of the lattice model we use the excited-state TBA approach. We consider in detail the case of the descendant at level 8. This paper is a contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”. The full collection is available at http://www.emis.de/journals/SIGMA/OPSF.html. Our special thanks go to M. Jimbo, T. Miwa and F. Smirnov with whom the work on this paper was started. Also we would like to thank F. G¨ohmann, A. Kl¨umper and S. Lukyanov for many stimulating discussions. We are grateful to the Volkswagen Foundation for financial support. 2011 Article Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States / H. Boos // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 82B20; 82B21; 82B23; 81T40; 81Q80 DOI:10.3842/SIGMA.2011.007 https://nasplib.isofts.kiev.ua/handle/123456789/146787 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We generalize the results of [Comm. Math. Phys. 299 (2010), 825-866] (hidden Grassmann structure IV) to the case of excited states of the transfer matrix of the six-vertex model acting in the so-called Matsubara direction. We establish an equivalence between a scaling limit of the partition function of the six-vertex model on a cylinder with quasi-local operators inserted and special boundary conditions, corresponding to particle-hole excitations, on the one hand, and certain three-point correlation functions of conformal field theory (CFT) on the other hand. As in hidden Grassmann structure IV, the fermionic basis developed in previous papers and its conformal limit are used for a description of the quasi-local operators. In paper IV we claimed that in the conformal limit the fermionic creation operators generate a basis equivalent to the basis of the descendant states in the conformal field theory modulo integrals of motion suggested by A. Zamolodchikov (1987). Here we argue that, in order to completely determine the transformation between the above fermionic basis and the basis of descendants in the CFT, we need to involve excitations. On the side of the lattice model we use the excited-state TBA approach. We consider in detail the case of the descendant at level 8. |
| format |
Article |
| author |
Boos, H. |
| spellingShingle |
Boos, H. Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Boos, H. |
| author_sort |
Boos, H. |
| title |
Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States |
| title_short |
Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States |
| title_full |
Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States |
| title_fullStr |
Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States |
| title_full_unstemmed |
Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States |
| title_sort |
fermionic basis in conformal field theory and thermodynamic bethe ansatz for excited states |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146787 |
| citation_txt |
Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States / H. Boos // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-11-24T18:45:31Z |
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2025-11-24T18:45:31Z |
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1849698477422936064 |