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Knot invariants from rational conformal field theories. (English) Zbl 0990.81694
Summary: A framework for studying knot and link invariants from any rational conformal field theory is developed. In particular, minimal models, superconformal models and \(W_{N}\) models are studied. The invariants are related to the invariants obtained from the Wess-Zumino models associated with the coset representations of these models. Possible Chern-Simons representation of these models is also indicated. This generalises the earlier work on knot and link invariants from Chern-Simons theories.

MSC:
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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References:
[1] Schwarz, A.S., New topological invariants arising in the theory of quantized fields, ()
[2] Witten, E., Commun. math phys., 121, 351, (1989)
[3] Isidro, J.M.; Labastida, J.M.F.; Ramallo, A.V.; Labastida, J.M.F.; Ramallo, A.V.; Labastida, J.M.F.; Llatas, P.M.; Ramallo, A.V., Phys. lett. B, Phys. lett. B, Nucl. phys. B, 348, 651, (1991)
[4] J.M. Isidro, J.M.F. Labastida and A.V. Ramallo, US/FT 9/92.
[5] Guadgnini, E., Int. J. mod. phys. A, 5, 877, (1992)
[6] Kaul, R.K.; Govindarajan, T.R.; Kaul, R.K.; Govindarajan, T.R., Nucl. phys. B, Nucl. phys. B, 393, 392, (1993)
[7] Ramadevi, P.; Govindarajan, T.R.; Kaul, R.K., Nucl. phys. B, 402, 548, (1993)
[8] R.K. Kaul, IMSc 93/3, Commun. Math. Phys. (in press).
[9] Yamagishi, K.; Ge, M-L; Wu, Y-S; Wu, Y.; Yamagishi, K.; Horne, J.H., Lett. math. phys., Int. J. modern phys. A, Nucl. phys. B, 334, 669, (1990)
[10] Jones, V.F.R.; Jones, V.F.R., Bull. AMS, Ann. math., 128, 335, (1987)
[11] Freyd, P.; Yetter, D.; Hoste, J.; Lickorish, W.B.R.; Millet, K.; Ocneanu, A.; Przytycki, J.H.; Traczyk, K.P., Bull. AMS, Kobe J. math., 4, 115, (1987)
[12] Kaul, R.K., Nucl. phys. B, 417, 267, (1994)
[13] Goddard, P.; Kent, A.; Olive, D.; Goddard, P.; Kent, A.; Olive, D.; Bardacki, K.; Halpern, M.B.; Halpern, M.B., Phys. lett. B, Commun. math. phys., Phys. rev. D, Phys. rev. D, 4, 2398, (1971)
[14] Ravanini, F., Mod. phys. lett. A, 3, 397, (1988)
[15] A. Gaume and G. Sierra, CERN preprint TH.5540/89.
[16] Kauffman, L.H., Knots and physics, (1991), World Scientific Singapore · Zbl 0749.57002
[17] Blok, B.; Yankielowicz, S., Nucl. phys. B, 321, 717, (1989)
[18] Moore, G.; Seiberg, N., Phys. lett. B, 220, 422, (1989)
[19] Lashkevich, M.Yu., Mod. phys. letts A, 8, 851, (1993)
[20] Mussardo, G.; Sotkov, G.; Stanishkov, M., Int. J. mod. phys. A, (1988)
[21] G. Mussardo, Thesis SISSA, Trieste, Italy;
[22] Kastor, D.; Matsuo, Y.; Yahikozawa, S., Nucl. phys. B, Phys. lett. B, 178, 211, (1986)
[23] Bilal, Adel, Nucl. phys. B, 330, 399, (1990)
[24] CERN preprint TH.6083/91.
[25] Fateev, V.A.; Zamolodchikov, A.B., Nucl. phys. B, 280, 644, (1987)
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