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The Chiral Space of Local Operators in SU(2)-Invariant Thirring Model

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Abstract

The space of local operators in the SU(2) invariant Thirring model (SU(2) ITM) is studied by the form factor bootstrap method. By constructing sets of form factors explicitly we define a susbspace of operators which has the same character as the level one integrable highest weight representation of . This makes a correspondence between this subspace and the chiral space of local operators in the underlying conformal field theory, the su(2) Wess-Zumino-Witten model at level one.

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References

  1. Babelon, O., Bernard, D., Smirnov, F.: Null-vectors in integrable field theory. Commun. Math. Phys. 186, 601–648 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cardy, J., Mussardo, G.: Form factors of descendent operators in perturbed conformal field theories. Nucl. Phys. B340, 387–402 (1990)

    Google Scholar 

  3. Christe, P.: Factorized characters and form factors of descendant operators in perturbed conformal systems. Int. J. Mod. Phys. A6, 5271–5286 (1991)

    Google Scholar 

  4. Jimbo, M., Miwa, T.: Quantum KZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime. J. Phys. A: Math. Gen. 29, 2923–2958 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kedem, R., McCoy, B., Melzer, E.: The sums of Rogers, Schur and Ramanujan and the Bose-Fermi correspondence in 1+1-dimensional quantum field theory. In: Recent Progress in Statistical Mechanics and Quantum Field Theory P. Bouwknegt, et al., (eds.), Singapore: World Scientific, 1995, pp. 195–219

  6. Koubek, A.: The space of local operators in perturbed conformal field theories. Nucl. Phys. B. 435, 703–734 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kac, V.: Infinite dimensional Lie algebras. Third edition. Cambridge: Cambridge University Press, 1992

  8. Kirillov, A.N., Smirnov, F.: A representation of the current algebra connected with the su(2)-invariant Thirring model. Phys. Lett. B 198, 506–510 (1987)

    Article  Google Scholar 

  9. Lukyanov, S.: Free field representation for massive integrable models. Commun. Math. Phys. 167, 183–226 (1995)

    MathSciNet  MATH  Google Scholar 

  10. Macdonald, I.G.: Symmetric functions and Hall polynomials. Second edition, Oxford: Oxford University Press, 1995

  11. Nakayashiki, A.: Residues of q-hypergeometric integrals and characters of affine Lie algebras. Commun. Math. Phys. 240, 197–241 (2003)

    Google Scholar 

  12. Nakayashiki, A., Pakuliak, S., Tarasov, V.: On solutions of the KZ and qKZ equations at level zero. Ann. Inst. Henri Poincaré 71, 459–496 (1999)

    MATH  Google Scholar 

  13. Nakayashiki, A., Takeyama, Y.: On form factors of SU(2) invariant Thirring model. In: MathPhys Odyssey 2001, Integrable Models and Beyond- in honor of Barry M. McCoy, Kashiwara, M. and Miwa, T., (eds.), Progr. Math. Phys., Basel-Boston: Birkhäuser, 2002, pp. 357–390

  14. Shintani, T.: On a Kronecker limit formula for real quadratic fields. J. Fac. Sci. Univ. Tokyo 24, 167–199 (1977)

    MATH  Google Scholar 

  15. Smirnov, F.: Lectures on integrable massive models of quantum field theory, In: Nankai Lectures on Mathem. Physics Ge,~M-L., Zhao,~B-H., (eds.), Singapore: World Scientific, 1990, pp. 1–68

  16. Smirnov, F.: Dynamical symmetries of massive integrable models. Int. J. Mod. Phys. A 7 Suppl. 1B, 813–837 (1992)

    Google Scholar 

  17. Smirnov, F.: Form factors in completely integrable models of quantum field theories. Singapore: World Scientific, 1992

  18. Smirnov, F.: Counting the local fields in SG theory. Nucl. Phys. B 453, 807–824 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  19. Tarasov, V.: Completeness of the hypergeometric solutions of the qKZ equations at level zero. Am. Math. Soc. Translations Ser. 2 201, 309–321 (2000)

    MATH  Google Scholar 

  20. Zamolodchikov, A.B.: Integrable field theory from conformal field theory. Adv. Stud. Pure Math. 19, 641–674 (1989)

    MATH  Google Scholar 

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  1. Faculty of Mathematics, Kyushu University, Ropponmatsu 4-2-1, Fukuoka, 810-8560, Japan

    Atsushi Nakayashiki

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  1. Atsushi Nakayashiki
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Correspondence to Atsushi Nakayashiki.

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Communicated by L. Takhtajan

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Nakayashiki, A. The Chiral Space of Local Operators in SU(2)-Invariant Thirring Model. Commun. Math. Phys. 245, 279–296 (2004). https://doi.org/10.1007/s00220-003-1013-3

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  • DOI: https://doi.org/10.1007/s00220-003-1013-3

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