Abstract
We define non-local conserved currents in massive current algebras in two dimensions. Our approach is algebraic and non-perturbative. The non-local currents give a quantum field realization of the Yangians. We show how the noncocommutativity of the Yangians is related to the non-locality of the currents. We discuss the implications of the existence of non-local conserved charges on theS-matrices.
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Belavin, A., Polyakov, A., Zamolodchikov, A.: Infinite dimensional symmetry in two-dimensional quantum field theory. Nucl. Phys.B241, 333–380 (1984)
Conformal invariance and applications to statistical mechanics. Itzykson, C., Saleur, H., Zuber, J.-B. (eds.) Singapore: World Scientific 1988
Zamolodchikov, A.B.: Integrable field theory from conformal field theory. Adv. Studies Pure Math.19, 641–674 (1989)
Zamolodchikov, A.B.: Integrals of motion in scaling 3-state Potts model field theory. Int. J. Mod. Phys. A3, 743–750 (1988)
Zamolodchikov, A.B.: Integrals of motion andS-matrix of the (scaled)T=T c Ising models with magnetic field. Int. J. Mod. Phys. A4, 4235 (1989)
Leclair, A.: Restricted sine-Gordon theory and the minimal conformal series. Phys. Lett.320 B, 103 (1989)
Smirnov, F.A.: The perturbedc<1 conformal field theories as reductions of sine-Gordon models. Int. J. Mod. Phys. A4, 4213 (1989)
Eguchi, T., Yang, S.K.: Deformations of conformal field theories and soliton equations. Phys. Lett.235B, 373 (1989)
Kupershmidt, B.A., Mathieu, P.: Quantum Korteweg-de Vries equations and perturbed conformal field theories. Phys. Lett.227B, 245–250 (1989)
Bernard, D., Leclair, A.: The fractional supersymmetric sine-Gordon models. Phys. Lett. B247, 309 (1990)
Zamolodchikov, A.B.: Preprint, Sept. 1989 (unpublished)
Bernard, D., Leclair, A.: Residual quantum symmetry in the restricted sine-Gordon theories. Nucl. Phys. B340, 721 (1990)
Ahn, C., Bernard, D., Leclair, A.: Fractional Supersymmetries in perturbed coset CFT's and integrable soliton theory. Nucl. Phys. B346, 409 (1990)
Drinfel'd, V.G.: Hopf algebras and the quantum Yang-Baxter equation. Sov. Math. Dokl.32, 254–258 (1985)
Kac, V.G.: Infinite dimensional Lie algebras. Cambridge: Cambridge University Press 1985
Knizhnik, V.G., Zamolodchikov, A.B.: Current algebras and Wess-Zumino models in two dimensions. Nucl. Phys. B247, 83–103 (1984)
Maillet, J.-M.: New integrable canonical structures in two-dimensional models. Nucl. Phys. B269, 54–76 (1986) and Hamiltonian structures for integrable classical theories from graded Kac-Moody algebras. Phys. Lett.167B, 401–405 (1986)
Lüscher, M., Pohlmeyer, K.: Scattering of massles lumps and non-local charges in the twodimensional classical non-linear σ-models. Nucl. Phys. B137, 46–54 (1978)
Brezin, E., et al.: Remarks about the existence of non-local charges in two-dimensional models. Phys. Lett.82B, 442–444 (1979)
Lüscher, M.: Quantum non-local charges and absence of particle production in the two-dimensional non-linear σ-models. Nucl Phys. B135, 1–19 (1978)
Coleman, S., Mandula, J.: All possible symmetries of theS-matrix. Phys. Rev.159, 1251 (1967)
Gradshteyn, I.S., Ryzhik, I.W.: Table of integrals, series and products. New York: Academic Press 1965
Zamolodchikov, A.B., Zamolodchikov, A.B.: FactorizedS-matrices in two dimensions as the exact solutions of certain relativistic quantum field theories. Ann. Phys.120, 253 (1979)
Bernard, D., Leclair, A.:Q-deformation of theSU(1,1), conformal ward identities andQ-string. Phys. Lett.227B, 417–423 (1989)
De Vega, H., Eichenherr, H., Maillet, J.M.: Yang-Baxter algebras of monodromy matrices in integrable quantum field theories. Nucl. Phys. B240[FS12], 377–399 (1984) and Classical and quantum algebras of non-local charges in σ-models. Commun. Math. Phys.92, 507–524 (1984)
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Communicated by K. Gawedzki
Laboratoire de la Direction des sciences de la matière du Commissariat à l'énergie atomique
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Bernard, D. Hidden Yangians in 2D massive current algebras. Commun.Math. Phys. 137, 191–208 (1991). https://doi.org/10.1007/BF02099123
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DOI: https://doi.org/10.1007/BF02099123