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Connecting Lattice and Relativistic Models via Conformal Field Theory

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Infinite Dimensional Algebras and Quantum Integrable Systems

Part of the book series: Progress in Mathematics ((PM,volume 237))

Abstract

We consider the quantum group invariant XXZ-model. In the infrared limit it describes a Conformal Field Theory (CFT) with modified energy-momentum tensor. The correlation functions are related to solutions of level −4 of the qKZ equations. We describe these solutions relating them to level 0 solutions. We further consider general matrix elements (form factors) containing local operators and asymptotic states. We explain that the formulae for solutions of the qKZ equations suggest a decomposition of these matrix elements with respect to states of the corresponding CFT.

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References

  1. M. Jimbo, K. Miki, T. Miwa, A. Nakayashiki, Phys. Lett. A168 (1992) 256–263.

    MathSciNet  Google Scholar 

  2. M. Jimbo, T. Miwa, J. Phys. A29 (1996) 2923–2958.

    MathSciNet  Google Scholar 

  3. V. Pasquier, H. Saleur, Nucl. Phys. B330 (1990) 523.

    MathSciNet  Google Scholar 

  4. J.M. Maillet, V. Terras, Nucl. Phys. B575 (2000) 627–647.

    MathSciNet  Google Scholar 

  5. N. Kitanine, J.M. Maillet, V. Terras, Nucl. Phys. B567 (2000), no. 3, 554–582.

    MathSciNet  Google Scholar 

  6. F.A. Smirnov, Int. J. Mod. Phys. A7, (1992) S813–858.

    Google Scholar 

  7. F.A. Smirnov, J. Phys. A19 (1986) L575–L578.

    Google Scholar 

  8. I. Frenkel, N. Reshetikhin, Comm. Math. Phys. 146 (1992) 1–60.

    Article  MathSciNet  Google Scholar 

  9. H.E. Boos, V.E. Korepin, J. Phys. A34 (2001) 5311–5316.

    MathSciNet  Google Scholar 

  10. H.E. Boos, V.E. Korepin, Evaluation of integrals representing correlators in XXX Heisenberg spin chain. in. MathPhys Odyssey 2001, Birkhäuser (2001) 65–108.

    Google Scholar 

  11. H.E. Boos, V.E. Korepin, F.A. Smirnov, Nucl. Phys. B 658/3 (2003) 417–439.

    MathSciNet  Google Scholar 

  12. N.Yu. Reshetikhin, F.A. Smirnov, Comm. Math. Phys., 1990, v. 132, p. 415.

    MathSciNet  Google Scholar 

  13. F.A. Smirnov, Form Factors in Completely Integrable Models of Quantum Field Theory. Adv. Series in Math. Phys. 14, World Scientific, Singapore (1992).

    Google Scholar 

  14. F.A. Smirnov, Lett. Math. Phys. 36 (1996) 267.

    Article  MATH  MathSciNet  Google Scholar 

  15. F.A. Smirnov, Nucl. Phys. B 453[FS] (1995) 807.

    Google Scholar 

  16. A. Nakayashiki, F.A. Smirnov, Comm. Math. Phys., 217 (2001), 623.

    Article  MathSciNet  Google Scholar 

  17. A. Nakayashiki, On the cohomology of theta divisor of hyperelliptic Jacobian. Contemporary mathematics, 309, in Integrable systems, topology and physics, M Guest et al. ed., AMS (2002).

    Google Scholar 

  18. L.D. Faddeev, Modular double of quantum group. math.qa/9912078, 11 pp.

    Google Scholar 

  19. P. Mejean, F.A. Smirnov IJMPA 12, 1997, no. 19, p. 3383–3395.

    MathSciNet  Google Scholar 

  20. O. Babelon, D. Bernard, F.A. Smirnov Commun. Math. Phys. 186, 1997, 601–648.

    Article  MathSciNet  Google Scholar 

  21. A. Nakayashiki, The Chiral Space of Local Operators in SU(2)-Invariant Thirring Model. math.QA/0303192.

    Google Scholar 

  22. M. Jimbo, T. Miwa, Y. Takeyama, Counting minimal form factors of the restricted sine-Gordon model math-ph/03030.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba, 277-8581, Japan

    H.E. Boos

  2. C.N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, NY, 11794-3840, USA

    V.E. Korepin

  3. LPTHE, Tour 16, 1-er étage, 4, pl. Jussieu, F-75252, Paris CEDEX 05, France

    F.A. Smirnov

Authors
  1. H.E. Boos
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  2. V.E. Korepin
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  3. F.A. Smirnov
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Editor information

Editors and Affiliations

  1. St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, Fontaka 27, 191011, St. Petersburg, Russia

    Petr P. Kulish

  2. Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Nenad Manojlovich

  3. IInd Institute for Theoretical Physics, University of Hamburg, Luruper Chaussee 149, 22761, Hamburg, Germany

    Henning Samtleben

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Boos, H., Korepin, V., Smirnov, F. (2005). Connecting Lattice and Relativistic Models via Conformal Field Theory. In: Kulish, P.P., Manojlovich, N., Samtleben, H. (eds) Infinite Dimensional Algebras and Quantum Integrable Systems. Progress in Mathematics, vol 237. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7341-5_5

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