Quantization of coset space σ-models coupled to two-dimensional gravity

Communications in Mathematical Physics

Volumn 190, Issue 2, 1997, Pages 411-457

  Korotkin, D ^a,b   Samtleben, H ^a,c  

^a UNIVERSITY OF HAMBURG   (Germany)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^c ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039466847     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050247     Document Type: Article

References (63)

1. Alekseev, A. Y.: Integrability in the Hamiltonian Chern-Simons theory. Algebra Anal. 6, 53-66 (1994)
2. Alekseev, A. Y., Grosse, H., and Schomerus, V.: Combinatorial quantization of the Hamiltonian Chern-Simons theory. Commun. Math. Phys. 172, 317-358 (1995)
3. Alekseev, A. Y., Grosse, H., and Schomerus, V.: Combinatorial quantization of the Hamiltonian Chern-Simons theory 2. Commun. Math. Phys. 174, 561-604 (1995)
4. Alekseev, A. Y., and Malkin, A. Z.: The hyperbolic moduli space of flat connections and the isomorphism of symplectic multiplicity spaces. Preprint dg-ga/9603017 (1996)
5. Ashtekar, A., and Pierri, M.: Probing quantum gravity through exactly soluble midi-superspaces I. J. Math. Phys. 37, 6250-6270 (1996)
6. Atiyah, M., and Bott, R.: The Yang-Mills equations over Riemann surfaces. Phil. Trans. R. Soc. Lond. A308, 523-615 (1982)
7. Axelrod, S., Witten, E., and Pietra, S. D.: Geometric quantization of Chern-Simons gauge theory. J. Diff. Geom. 33, 787-902 (1991)
8. Bais, F.A., and Sasaki, R.: On the algebraic structure of selfdual gauge fields and sigma models. Nucl. Phys. B227, 75-120 (1983)
9. Barvinsky, A., and Kunstatter, G.: Exact physical black hole states in generic 2-d dilaton gravity. Phys. Lett. B389, 231-237 (1996)
10. Belinskii, V., and Zakharov, V.: Integration of the Einstein equations by means of the inverse scattering problem technique and construction of exact soliton solutions. Sov. Phys. JETP 48, 985-994 (1978)
11. Bobenko, A.I.: Surfaces in terms of 2 by 2 matrices. Old and new integrable cases. In: A. Fordy and J.C. Wood (eds.), Harmonic Maps and Integrable Systems. Vieweg, 1993
12. Breitenlohner, P., and Maison, D.: On the Geroch group. Ann. Inst. H. Poincaré. Phys. Théor. 46, 215-246 (1987)
13. Breitenlohner, P., Maison, D., and Gibbons, G.: Four-dimensional black holes from Kaluza-Klein theories. Commun. Math. Phys. 120, 295-333 (1988)
14. Callan, C., Giddings, S., Harvey, J., and Strominner, A.: Evanescent black holes. Phys. Rev. D45, R 1005-1009 (1992)
15. Courant, R., and Hilbert, D.: Methoden der mathematischen Physik. Berlin: Springer Verlag, 1931
16. Cvetič, M., and Hull, C. M.: Black holes and U duality. Nucl. Phys. B480, 296-316 (1996)
17. Cvetič, M., and Youm, D.: BPS saturated dyonic black holes of N=8 supergravity vacua. In: E. Gava, K. Narain, and C. Vafa (eds.), S Duality and Mirror Symmetry, Nucl. Phys. B (Proc. Supl.) vol. 46, Amsterdam: North-Holland, 1995
18. Dickey, L. A.: Field theoretical (multitime) Lagrange-Hamiltonian formalism and integrable equations. In: O. Babelon, P. Cartier and Y. Kosmann-Schwarzbach (eds.), Lectures on Integrable Systems. Singapore: World Scientific, 1994
19. Dirac, P.A.M.: Lectures on Quantum Mechanics. New York: Academic Press, 1967
20. Drinfeld, V.: Hopf algebras and the quantum Yang-Baxter equation. Soviet Math. Dokl. 32, 254-258 (1985)
21. Drinfeld, V.: Quasi-Hopf algebras and Knizhnik-Zamolodchikov equations. In: Problems of modern quantum held theory (Alushta 1989), pp. 1-13. Berlin: Springer-Verlag, 1989
22. Drinfeld, V.: Quasi-Hopf algebras. Leningrad Math. J. 1, 1419-1457 (1990)
23. Elitzur, S., Moore, G., Schwimmer, A., and Seiberg, N.: Remarks on the canonical quantization of the Chern-Simons-Witten theory. Nucl. Phys. B326, 108-134 (1989)
24. Faddeev, L.: Integrable models in (1+1) dimensional quantum field theory. In: J.-B. Zuber and R. Stora (eds.), Les Houches, Session XXXIX, Recent advances in field theory and statistical mechanics, Amsterdam: North-Holland, 1984, pp. 561-608
25. Faddeev, L.: From integrable models to conformal field theories via quantum groups. In: L. Ibert and M. Rodriguez (eds.), Proceedings of NATO ASI and XXII GIFT International Seminar on Recent Problems in Mathematical Physics, Salamanca, Spain 1992, Dordrecht: Kluwer Academic Publishers, 1992, pp. 1-24
26. Faddeev, L., and Takhtajan, L.: Hamiltonian Methods in the Theory of Solitons. Berlin: Springer-Verlag, 1987
27. Filippov, A.: Exact solutions of (1+1)-dimensional dilaton gravity coupled to matter. Mod. Phys. Lett. A11, 1691-1704 (1996)
28. Fock, V.V., and Rosly, A.A.: Poisson structures on moduli of flat connections on Riemann surfaces and r-matrices. Preprint ITEP 72-92, Moscow (1992)
29. Frenkel, I., and Reshetikhin, N.: Quantum affine algebras and holonomic difference equations. Commun. Math. Phys. 146, 1-60 (1992)
30. Gal'tsov, D.V.: Integrable systems in stringy gravity. Phys. Rev. Lett. 74, 2863-2866 (1995)
31. Gawȩdzki, K., and Kupiainen, A.: SU(2) Chem-Simons theory at genus zero. Commun. Math. Phys. 135, 531-546 (1991)
32. Gegenberg, J., Kunstatter, G., and Louis-Martinez, D.: Observables for two-dimensional black holes. Phys. Rev. D51, 1781-1786 (1995)
33. Geroch, R.: A method for generating solutions of Einstein's equations. J. Math. Phys. 12, 918-924 (1971)
34. Goldman, W.: Invariant functions on Lie groups and Hamiltonian flows of surfaces group representations. Invent. Math. 85, 263-302 (1986)
35. Hennaux, M., and Teitelboim, C.: Quantization of Gauge Systems. Princeton: Princeton University Press, 1992
36. Hitchin, N.: Frobenius manifolds, to appear
37. Jimbo, M.: A q-difference analogue of u(g) and the Yang-Baxter equation. Lett. Math. Phys. 10, 63-69 (1985)
38. Jimbo, M., Miwa, T., Môri, Y., and Sato, M.: Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent. Physica 1D, 80-158 (1980)
39. Jimbo, M., Miwa, T., and Ueno, K.: Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. Physica 2D, 306-352 (1981)
40. Julia, B.: Group disintegrations. In: S. Hawking and M. Rocek (eds.), Superspace and Supergravity, Cambridge: Cambridge University Press, 1980, pp. 331-350
41. Julia, B.: Application of supergravity to gravitation theories. In: V. D. Sabbata and E. Schmutzer (eds.), Unified Field Theories in more than 4 Dimensions, Singapore: World Scientific, 1983, pp. 215-236
42. Julia, B., and Nicolai, H.: Conformal internal symmetry of 2-D sigma models coupled to gravity and a dilaton. Nucl. Phys. B482, 431-465 (1996)
43. Kassel, C.: Quantum Groups. No. 155 in Graduate texts in mathematics. Berlin: Springer-Verlag, 1995
44. Kastrup, H.: Canonical theories of lagrangian dynamical systems in physics. Phys. Rep. 101, 1-167 (1983)
45. Knizhnik, V. and Zamolodchikov, A. B.: Current algebra and Wess-Zumino model in two-dimensions. Nucl. Phys. B247, 83-103 (1984)
46. Korepin, V. E., Bogoliubov, N. M., and Izergin, A. G.: Quantum inverse scattering method and correlation functions. Cambridge: Cambridge University Press, 1993
47. Korotkin, D., and Nicolai, H.: Separation of variables and Hamiltonian formulation for the Ernst equation. Phys. Rev. Lett. 74, 1272-1275 (1995)
48. Korotkin, D., and Nicolai, H.: An integrable model of quantum gravity. Phys. Lett. B356, 211-216 (1995)
49. Korotkin, D., and Nicolai, H.: Isomonodromic quantization of dimensionally reduced gravity. Nucl. Phys. B475, 397-439 (1996)
50. Korotkin, D., and Samtleben, H.: On the quantization of isomonodromic deformations on the torus. Int. J. Mod. Phys. A12, 2013-2029 (1997)
51. Korotkin, D., and Samtleben, H.: Poisson realization and quantization of the Geroch group. Preprint DESY-96-245, gr-qc/9611061 (1996), Class. Quantum Grav. to appear
52. Kuchař, K.: Canonical Quantization of Cylindrical Gravitational Waves. Phys. Rev. D4, 955-986 (1971)
53. Maharana, J.: Symmetries of the dimensionally reduced string effective action. Mod. Phys. Lett. A11, 9-17 (1996)
54. Maison, D.: Are the stationary, axially symmetric Einstein equations completely integrable? Phys. Rev. Lett. 41, 521-522 (1978)
55. Nicolai, H.: Two-dimensional gravities and supergravities as integrable systems. In: H. Mitter and H. Gausterer (eds.), Recent Aspects of Quantum Fields. Berlin: Springer-Verlag, 1991
56. Nicolai, H., Korotkin, D., and Samtleben, H.: Integrable classical and quantum gravity. To appear in: G. Mack, G. t'Hooft, A. Jaffe, H. Mitter and R. Stora (eds.), Quantum Fields and Quantum Space Time, Proceedings NATO-ASI. Cargèse 1996. New York: Plenum Press, 1997
57. Reshetikhin, N.: The Knizhnik-Zamolodchikov system as a deformation of the isomonodromy problem. Lett. Math. Phys. 26, 167-177 (1992)
58. Schemmel, M.: Diploma thesis, Hamburg (1997)
59. Semenov-Tian-Shansky, M.A.: Monodromy map and classical r-matrices. J. Math. Sci. 77, 3236-3242 (1995); translation from Zap. Nauchn. Semi. POMI 200, 156-166 (1992)
60. Semenov-Tian-Shansky, M.A.: Monodromy map and classical r-matrices. J. Math. Sci. 77, 3236-3242 (1995); translation from Zap. Nauchn. Semi. POMI 200, 156-166 (1992)
61. Smirnov, F. A.: Dynamical symmetries of massive integrable models, 1. Form-factor bootstrap equations as a special case of deformed Knizhnik-Zamolodchikov equations. Int. J. Mod. Phys. A7, suppl. 1B, 813-838 (1991)
62. Witten, E.: Quantum field theory and the Jones polynomial. Commun. Math. Phys. 121, 351-399 (1989)
63. Zamolodchikov, A.B., and Fateev, V.A.: Operator algebras and correlation functions in the two-dimensional Wess-Zumino SU (2) × SU (2) chiral model. Yad. Fiz. 43, 1031-1044 (1986)