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Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States

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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Main Author: Boos, H.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/146787
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spelling irk-123456789-1467872019-02-12T01:24:26Z 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. 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 http://dspace.nbuv.gov.ua/handle/123456789/146787 en Symmetry, Integrability and Geometry: Methods and Applications 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 http://dspace.nbuv.gov.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
work_keys_str_mv AT boosh fermionicbasisinconformalfieldtheoryandthermodynamicbetheansatzforexcitedstates
first_indexed 2023-05-20T17:25:40Z
last_indexed 2023-05-20T17:25:40Z
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