Abstract
The traces over infinite-dimensional representations of the central extended Yangian double for the product of operators which intertwine these representations are calculated. For the special combinations of the intertwining operators, the traces are identified with form factors of local operators in the SU(2)-invariant Thirring model. This identification is based on the identities which are deformed analogs of the Gauss–Manin connection identities for the hyperelliptic curves.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barnes, E.W.: On the theory of the multiple gamma function, Trans. Cambridge Philos. Soc. 19 (1904), 374-425.
Bateman, H. and Erdélyi, A.: Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York, 1953.
Bernard, D. and A. LeClair.: The quantum double in integrable quantum field theories, Nuclear Phys. B 399 (1993), 709-748.
Chervov, A.: Traces of creating-annihilating operators and Fredholm's formulas, Preprint ITEPTH 8/97, q-alg/9703017.
Drinfeld, V. G.: Quantum groups, in: Proc. Internat. Congress of Mathematicians, Berkeley, 1987, pp. 798-820.
Frenkel, I.B. and Jing, N.: Vertex operators of quantum affine algebras, Proc. Nat. Acad. Sci. USA 85 (1988), 9373-9377.
Iohara, K.: Bosonic representations of Yangian double DY ħ(g) with g = glN; slN, Preprint q-alg/9603033.
Jimbo, M. and Miwa, T.: Algebraic Analysis of Solvable Lattice Models, Conference Board of the Math. Sci., Regional Conference Series in Math. 85 (1995).
Jimbo, M., Kojima, T., Miwa, T., and Quano, Y.-H.: Smirnov's integrals and quantum Knizhnik-Zamolodchikov equation of level 0, J. Phys. A 27 (1994) 3267.
Khoroshkin, S.: Central extension of the Yangian double, Preprint q-alg/9602031.
Khoroshkin, S. and Tolstoy, V.: Yangian double, Lett. Math. Phys. 36 (1996), 373-402.
Khoroshkin, S., Lebedev, D. and Pakuliak, S.: Intertwining operators for the central extension of the Yangian double, Phys. Lett. A 222 (1996), 381-392.
Khoroshkin, S., Lebedev, D. and Pakuliak, S.: Traces of intertwining operators for the Yangian double, Preprint ITEP-TH-8/96, BONN-TH-96-03, q-alg/9605039.
Lukyanov, S.: Free field representation for massive integrable models, Comm. Math. Phys. 167 (1995), 183-226.
Manin, Yu. I.: Algebraic curves over fields with differentiation, Izv. Akad. Nauk. SSSR. Ser. Mat. 22 (1958) 737-756.
Nakayashiki, A.: Some integral formulas for the solutions of the sl2 dKZ equation with level-4, Internat. J. Modern Phys. A 9(32) (1994), 5673-5687.
Smirnov, F.A.: Form Factors in Completely Integrable Field Theories, World Scientific, Singapore, 1992.
Smirnov, F.A.: Dinamical symmetries of massive integrable models, J. Modern Phys. A, 7 suppl. 1B (1992), 813-838.
Smirnov, F.A.: On the deformation of Abelian integrals, Lett. Math. Phys. 36 (1996), 267-275.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
KHOROSHKIN, S., LEBEDEV, D. & PAKULIAK, S. Traces of Intertwining Operators for the Yangian Double. Letters in Mathematical Physics 41, 31–47 (1997). https://doi.org/10.1023/A:1007372113466
Issue Date:
DOI: https://doi.org/10.1023/A:1007372113466