Conformal internal symmetry of 2d σ-models coupled to gravity and a dilaton

Nuclear Physics B

Volumn 482, Issue 1-2, 1996, Pages 431-465

  Julia, B ^a   Nicolai, H ^b  

^a LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

^b UNIVERSITY OF HAMBURG   (Germany)

Author keywords

Dilaton; Geroch; Integrable system; Kac Moody; Sigma model; Virasoro

Indexed keywords

EID: 0030599650     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(96)00551-2     Document Type: Article

References (56)

1. [1] R. Geroch, J. Math. Phys. 12 (1971) 918; 13 (1972) 394.
2. [1] R. Geroch, J. Math. Phys. 12 (1971) 918; 13 (1972) 394.
3. [2] See e.g. Solutions of Einstein's Equations: Techniques and results, eds. C. Hoenselaers and W. Dietz (Springer, Berlin, 1984) and references quoted in Refs. [6,11].
4. [3] D. Maison, Phys. Rev. Lett. 41 (1978) 521; V. Belinskii and V. Zakharov, Sov. Phys. JETP 48 (1978) 985.
5. [3] D. Maison, Phys. Rev. Lett. 41 (1978) 521; V. Belinskii and V. Zakharov, Sov. Phys. JETP 48 (1978) 985.
6. [4] K. Pohlmeyer, Com. Math. Phys. 46 (1976) 207; M. Lüscher and K. Pohlmeyer, Nucl. Phys. B 137 (1978) 46.
7. [4] K. Pohlmeyer, Com. Math. Phys. 46 (1976) 207; M. Lüscher and K. Pohlmeyer, Nucl. Phys. B 137 (1978) 46.
8. [5] E. Cremmer and B. Julia, Nucl. Phys. B 159 (1979) 141.
9. [6] B. Julia, in Superspace and Supergravity, ed. S.W. Hawking and M. Rocek (Cambridge Univ. Press, Cambridge, 1980); in Proc. 1982 Chicago AMS-SIAM Conf., Lect. in App. Math. 21 (1985) 355; in Vertex Operators in Mathematics and Physics, ed. J. Lepowsky, S. Mandelstam and I.M. Singer (Springer, Berlin, 1984).
10. [6] B. Julia, in Superspace and Supergravity, ed. S.W. Hawking and M. Rocek (Cambridge Univ. Press, Cambridge, 1980); in Proc. 1982 Chicago AMS-SIAM Conf., Lect. in App. Math. 21 (1985) 355; in Vertex Operators in Mathematics and Physics, ed. J. Lepowsky, S. Mandelstam and I.M. Singer (Springer, Berlin, 1984).
11. [6] B. Julia, in Superspace and Supergravity, ed. S.W. Hawking and M. Rocek (Cambridge Univ. Press, Cambridge, 1980); in Proc. 1982 Chicago AMS-SIAM Conf., Lect. in App. Math. 21 (1985) 355; in Vertex Operators in Mathematics and Physics, ed. J. Lepowsky, S. Mandelstam and I.M. Singer (Springer, Berlin, 1984).
12. [7] B. Julia, in Unified Field Theories in more than 4 Dimensions including Exact Solutions, ed. V. de Sabbata and E. Schmutzer (World Scientific, Singapore, 1983).
13. [8] B. Julia, in Johns Hopkins Workshop on Current Problems in Particle Physics: Unified Theories and Beyond (Johns Hopkins University, Baltimore, 1981).
14. [9] On the mathematical history, see H. Garland, The arithmetic theory of Loop groups, Pub. Math. de l'IHES 52 (1980) and for an early physical work realizing current algebras, see K. Bardakci and M. Halpern, Phys. Rev. D 3 (1971) 2493.
15. [9] On the mathematical history, see H. Garland, The arithmetic theory of Loop groups, Pub. Math. de l'IHES 52 (1980) and for an early physical work realizing current algebras, see K. Bardakci and M. Halpern, Phys. Rev. D 3 (1971) 2493.
16. [10] P Breitenlohner and D. Maison, in |2| and Ann. Inst. Poincaré 46 (1987) 215.
17. [11] H. Nicolai, in Recent Aspect of Quantum Fields, Proc., Schladming 1991, ed. H. Mitter and H. Gausterer (Springer Verlag, 1991).
18. [12] L. Dolan, Phys. Rev. Lett. 47 (1981) 1371; H. Eichenherr and M. Forger, Com. Math. Phys. 82 (1981) 227; Y.S. Wu, Nucl. Phys. B 211 (1983) 160.
19. [12] L. Dolan, Phys. Rev. Lett. 47 (1981) 1371; H. Eichenherr and M. Forger, Com. Math. Phys. 82 (1981) 227; Y.S. Wu, Nucl. Phys. B 211 (1983) 160.
20. [12] L. Dolan, Phys. Rev. Lett. 47 (1981) 1371; H. Eichenherr and M. Forger, Com. Math. Phys. 82 (1981) 227; Y.S. Wu, Nucl. Phys. B 211 (1983) 160.
21. [13] CM. Cosgrove, J. Math. Phys. 21 (1980) 2417.
22. [14] Bo-Yu Hou and Wei Li, Lett. Math. Phys. 13 (1987) 1; Class. Quantum Grav. 6 (1989) 163.
23. [14] Bo-Yu Hou and Wei Li, Lett. Math. Phys. 13 (1987) 1; Class. Quantum Grav. 6 (1989) 163.
24. [15] D. Maison, preprint MPI-PAE/PTh 80/88 (1988); P. Breitenlohner and D. Maison, unpublished.
25. [15] D. Maison, preprint MPI-PAE/PTh 80/88 (1988); P. Breitenlohner and D. Maison, unpublished.
26. [16] J.H. Schwarz, Nucl. Phys. B454 (1995) 427.
27. [17] R. Ward. Gen. Rel. Grav. 15 (1983) 105; L.J. Mason and N.M.J. Woodhouse, Non-linearity 1 (1988) 73; J. Fletcher and N.M.J. Woodhouse, in Twistors in Mathematical Physics, ed. T.N. Bailey and R.J. Baston, LMS Lecture Notes, Series 56 (Cambridge University Press, 1990): F. A. Bais and R. Sasaki, Nucl. Phys. B 195 (1982) 522; Nucl. Phys. B 227 (1983) 75 L. Mason, S. Chakravarty and E.T. Newman, J. Math. Phys. 29 (1989) 1005.
28. [17] R. Ward. Gen. Rel. Grav. 15 (1983) 105; L.J. Mason and N.M.J. Woodhouse, Non-linearity 1 (1988) 73; J. Fletcher and N.M.J. Woodhouse, in Twistors in Mathematical Physics, ed. T.N. Bailey and R.J. Baston, LMS Lecture Notes, Series 56 (Cambridge University Press, 1990): F. A. Bais and R. Sasaki, Nucl. Phys. B 195 (1982) 522; Nucl. Phys. B 227 (1983) 75 L. Mason, S. Chakravarty and E.T. Newman, J. Math. Phys. 29 (1989) 1005.
29. [17] R. Ward. Gen. Rel. Grav. 15 (1983) 105; L.J. Mason and N.M.J. Woodhouse, Non-linearity 1 (1988) 73; J. Fletcher and N.M.J. Woodhouse, in Twistors in Mathematical Physics, ed. T.N. Bailey and R.J. Baston, LMS Lecture Notes, Series 56 (Cambridge University Press, 1990): F. A. Bais and R. Sasaki, Nucl. Phys. B 195 (1982) 522; Nucl. Phys. B 227 (1983) 75 L. Mason, S. Chakravarty and E.T. Newman, J. Math. Phys. 29 (1989) 1005.
30. [17] R. Ward. Gen. Rel. Grav. 15 (1983) 105; L.J. Mason and N.M.J. Woodhouse, Non-linearity 1 (1988) 73; J. Fletcher and N.M.J. Woodhouse, in Twistors in Mathematical Physics, ed. T.N. Bailey and R.J. Baston, LMS Lecture Notes, Series 56 (Cambridge University Press, 1990): F. A. Bais and R. Sasaki, Nucl. Phys. B 195 (1982) 522; Nucl. Phys. B 227 (1983) 75 L. Mason, S. Chakravarty and E.T. Newman, J. Math. Phys. 29 (1989) 1005.
31. [17] R. Ward. Gen. Rel. Grav. 15 (1983) 105; L.J. Mason and N.M.J. Woodhouse, Non-linearity 1 (1988) 73; J. Fletcher and N.M.J. Woodhouse, in Twistors in Mathematical Physics, ed. T.N. Bailey and R.J. Baston, LMS Lecture Notes, Series 56 (Cambridge University Press, 1990): F. A. Bais and R. Sasaki, Nucl. Phys. B 195 (1982) 522; Nucl. Phys. B 227 (1983) 75 L. Mason, S. Chakravarty and E.T. Newman, J. Math. Phys. 29 (1989) 1005.
32. [17] R. Ward. Gen. Rel. Grav. 15 (1983) 105; L.J. Mason and N.M.J. Woodhouse, Non-linearity 1 (1988) 73; J. Fletcher and N.M.J. Woodhouse, in Twistors in Mathematical Physics, ed. T.N. Bailey and R.J. Baston, LMS Lecture Notes, Series 56 (Cambridge University Press, 1990): F. A. Bais and R. Sasaki, Nucl. Phys. B 195 (1982) 522; Nucl. Phys. B 227 (1983) 75 L. Mason, S. Chakravarty and E.T. Newman, J. Math. Phys. 29 (1989) 1005.
33. [18] J. Milnor, Relativity, Groups and Topology II, ed. B.S. De Witt and R. Stora (Elsevier, 1984).
34. [19] A. Pressley and G. Segal, Loop Groups (Oxford University Press, 1986).
35. [20] D. Korotkin, Theor. Math. Phys. 77 (1989) 1018; D. Korotkin and V. Matveev, St. Petersburg Math. J. 1 (1990) 379.
36. [20] D. Korotkin, Theor. Math. Phys. 77 (1989) 1018; D. Korotkin and V. Matveev, St. Petersburg Math. J. 1 (1990) 379.
37. [21] D. Korotkin and H. Nicolai, Nucl. Phys. B 429 (1994) 229.
38. [22] S. Helgason, Differential Geometry and Symmetric Spaces (Academic Press, 1962).
39. [23] V. Kac, Infinite Dimensional Lie Algebras (Cambridge University Press, 1990).
40. [24] B. C. Xanthopoulos, J. Math. Phys. 22 (1981) 1254, asym. flat case; F. Ernst and I. Hauser, J. Math. Phys. 22 (1981) 1051.
41. [24] B. C. Xanthopoulos, J. Math. Phys. 22 (1981) 1254, asym. flat case; F. Ernst and I. Hauser, J. Math. Phys. 22 (1981) 1051.
42. [25] Yu. A. Neretin, Funct. Anal. and Appl. 21 (1987) 160, Math. USSR Sbornik 67 (1989) 75; see also: R. Goodman and N. Wallach, J. Reine u. Angew. Math. 347 (1984) 69.
43. [25] Yu. A. Neretin, Funct. Anal. and Appl. 21 (1987) 160, Math. USSR Sbornik 67 (1989) 75; see also: R. Goodman and N. Wallach, J. Reine u. Angew. Math. 347 (1984) 69.
44. [25] Yu. A. Neretin, Funct. Anal. and Appl. 21 (1987) 160, Math. USSR Sbornik 67 (1989) 75; see also: R. Goodman and N. Wallach, J. Reine u. Angew. Math. 347 (1984) 69.
45. [26] A.A. Kirillov, Funct. Anal. and Appl. 21 (1987) 122; A.A. Kirillov and D.V. Yur'ev, Funct. Anal. and Appl. 21 (1987) 284.
46. [26] A.A. Kirillov, Funct. Anal. and Appl. 21 (1987) 122; A.A. Kirillov and D.V. Yur'ev, Funct. Anal. and Appl. 21 (1987) 284.
47. [27] G. Segal, in Differential Geometric Methods in Theoretical Physics, ed. K. Bleuler and M. Werner (Kluwer, Dordrecht, 1988).
48. [28] D. Gross and A. Jevicki, Nucl. Phys. B 283 (1987) 1.
49. [29] D. Kramer, H. Stephani, M. MacCallum and E. Herlt, Exact Solutions of Einstein's Field Equations (Cambridge University Press, 1980).
50. [30] H. Nicolai, Nucl. Phys. B 414 (1994) 299.
51. [31] L. Faddeev and L. Takhtajan, Hamiltonian Methods in the Theory of Solitons (Springer, Berlin, 1986); V. Korepin, M. Bogoliubov and A. Izergin, Quantum Inverse scattering Method and Correlation Functions (Cambridge Univ. Press, Cambridge, 1993).
52. [31] L. Faddeev and L. Takhtajan, Hamiltonian Methods in the Theory of Solitons (Springer, Berlin, 1986); V. Korepin, M. Bogoliubov and A. Izergin, Quantum Inverse scattering Method and Correlation Functions (Cambridge Univ. Press, Cambridge, 1993).
53. [32] M.C. Davies, P.J. Houston, J.M. Leinaas and A.J. Macfarlane, Phys. Lett. B 119 (1982) 187;
54. H.J. de Vega, H. Eichenherr and J.M. Maillet, Commun. Math. Phys. 92 (1984) 507.
55. [33] D. Korotkin and H. Nicolai, Phys. Rev. Lett. 74 (1995) 1272; Phys. Lett. B 356 (1995) 211.
56. [33] D. Korotkin and H. Nicolai, Phys. Rev. Lett. 74 (1995) 1272; Phys. Lett. B 356 (1995) 211.