Integrability and canonical structure of d = 2, N = 16 supergravity

Nuclear Physics B

Volumn 533, Issue 1-3, 1998, Pages 210-242

  Nicolai, H ^a   Samtleben, H ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

Geroch group; Integrable systems; Superconformal algebras; Supergravity; Yangian symmetry

Indexed keywords

EID: 0032538749     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(98)00496-9     Document Type: Article

References (46)

1. [1] H. Nicolai, The integrability of N = 16 supergravity, Phys. Lett. B 194 (1987) 402.
2. [2] H. Nicolai and N.P. Warner, The structure of N = 16 supergravity in two dimensions, Commun. Math. Phys. 125 (1989) 369.
3. [3] H. Nicolai, New linear systems for 2d Poincaré supergravities, Nucl. Phys, B 414 (1994) 299.
4. [4] B. Julia, Group disintegrations, in Superspace and Supergravity, eds. S.W. Hawking and M. Rocek (Cambridge Univ. Press, Cambridge, 1981).
5. [5] E. Cremmer, B. Julia and J. Scherk, Supergravity theory in eleven-dimensions, Phys. Lett. B 76 (1978) 409.
6. [6] E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys. B 159 (1979) 141.
7. [7] H. de Vega, H. Eichenherr and J. Maillet, Classical and quantum algebras of non-local charges in σ models, Commun. Math. Phys. 92 (1984) 507.
8. [8] D. Korotkin and H. Samtleben, Yangian symmetry in integrable quantum gravity, Nucl. Phys. B 527 (1998) 657, hep-th/9710210.
9. [9] O. Babelon and D. Bernard, Dressing symmetries, Commun. Math. Phys. 149 (1992) 279.
10. [10] J.-H. Lu, Moment maps at the quantum level, Commun. Math. Phys. 157 (1993) 389.
11. [11] N. Marcus and J.H. Schwarz, Three-dimensional supergravity theories, Nucl. Phys. B 228 (1983) 145.
12. [12] R. Dick, Conformal gauge fixing in Minkowski space, Lett. Math. Phys. 18 (1989) 67.
13. [13] R. Dick, Topological aspects of chiral fields in two-dimensions and superstring vertices, Fortschr. Phys. 40 (1992) 519.
14. [14] D. Korotkin and H. Nicolai, Isomonodromic quantization of dimensionally reduced gravity, Nucl. Phys. B 475 (1996) 397.
15. [15] D. Kramer, H. Stephani, E. Herlt and M. MacCallum, Exact Solutions of Einstein's Field Equations (Cambridge Univ. Press, Cambridge, 1980).
16. [16] A. Einstein and N. Rosen, On gravitational waves, J. Franklin Inst. 223 (1937) 43.
17. [17] R. Gowdy, Vacuum space-times with two-parameter spacelike isometry group and compact invariant hypersurfaces: topologies and boundary conditions, Ann. Phys. 83 (1974) 203.
18. [18] B.-Y. Hou and W. Lee, Virasoro algebra in the solution space of the Ernst equation, Lett. Math. Phys. 13 (1987) 1.
19. [19] D. Maison, Geroch group and inverse scattering method, Preprint MPI-PAE/PTh-80/88, Munich (1988).
20. [20] B. Julia and H. Nicolai, Conformal internal symmetry of 2d σ-models coupled to gravity and a dilaton, Nucl. Phys. B 482 (1996) 431.
21. [21] P. Ramond and J.H. Schwarz, Classification of dual model gauge algebras, Phys. Lett. B 64 (1976) 75.
22. [22] P. van Nieuwenhuizen, Supergravity, Phys. Rept. 68 (1981) 189.
23. [23] M.F. Sohnius, Soft gauge algebras, Z. Phys. C 18 (1983) 229.
24. [24] D. Maison, Are the stationary, axially symmetric Einstein equations completely integrable?, Phys. Rev. Lett. 41 (1978) 521.
25. [25] V. Belinskii and V. Zakharov, Integration of the Einstein equations by means of the inverse scattering problem technique and construction of exact soliton solutions, Sov. Phys. JETP 48 (1978) 985.
26. [26] P. Breitenlohner and D. Maison, On the Geroch group, Ann. Inst. H. Poincaré. Phys. Théor. 46 (1987) 215.
27. [27] B. Julia, Infinite Lie Algebras in Physics, in: Unified Field Theories and Beyond, Johns Hopkins Workshop on Current Problems in Particle Theory, Johns Hopkins Univ., Baltimore, USA (1981).
28. [28] E. Corrigan and C. Zachos, Non-local charges for the supersymmetric sigma model, Phys. Lett. 88B (1979) 273.
29. [29] T.L. Curtright and C.K. Zachos, Non-local currents for supersymmetric non-linear models, Phys. Rev, D 21 (1980) 411.
30. [30] E. Abdalla and M. Forger, Integrable non-linear sigma models with fermions, Commun. Math. Phys. 104 (1986) 123.
31. [31] L.E. Saltini and A. Zadra, Algebra of non-local charges in supersymmetric non-linear sigma models, Int. J. Mod. Phys. A 12 (1997) 419.
32. [32] L. Faddeev, E. Sklyanin and L. Takhtajan, Quantum inverse scattering method, Theoret. Math. Phys. 40 (1979) 194.
33. [33] V. Drinfel'd, Hopf algebras and the quantum Yang-Baxter equation, Soviet Math. Dokl. 32 (1985) 254.
34. [34] D. Bernard, Hidden Yangians in 2D massive current algebras. Commun. Math. Phys. 137 (1991) 191.
35. [35] M. Lüscher and K. Pohlmeyer, Scattering of massless lumps and non-local charges in the two-dimensional classical non-linear σ-model, Nucl. Phys. B 137 (1978) 46.
36. [36] M.C. Davies, P.J.. Houston, J.M. Leinaas and A.J. Macfarlane, Hidden symmetries as canonical transformations for the chiral model, Phys. Lett. 119B (1982) 187.
37. [37] M. Semenov-Tian-Shansky, Dressing transformations and Poisson group actions, Publ. RIMS, Kyoto Univ. 21 (1985) 1237.
38. [38] D. Korotkin and H. Samtleben, Poisson realization and quantization of the Geroch group. Class. Quantum Grav. 14 (1997) L151.
39. [39] D. Bernard and B. Julia, Twisted self-duality of dimensionally reduced gravity and vertex operators, Preprint SPhT-97/113, LPT ENS-97/41, hep-th/9712254 (1997).
40. [40] H. Nicolai, Two-dimensional gravities and supergravities as integrable systems, in: Recent Aspects of Quantum Fields, ed. H. Mitter and H. Gausterer (Springer, Berlin, 1991).
41. [41] F.A. Smirnov, Form factors in completely integrable models of quantum field theory, No. 14, in Advanced series in Mathematical Physics (World Scientific, Singapore, 1992).
42. [42] V. Chart and A. Pressley, Fundamental representations of Yangians and singularities of R-matrices, J. Reine Angew. Math. 417 (1991) 87.
43. [43] B. de Wit, H.J. Matschull and H. Nicolai, Physical states in d = 3, N = 2 supergravity, Phys. Lett. B 318 (1993) 115.
44. [44] S.M. Carroll, D.Z. Freedman, M.E. Ortiz and D.N. Page, Physical states in canonically quantized supergravity, Nucl. Phys. B 423 (1994) 661.
45. [45] J. Polchinski, Tasi lectures on D-branes, Preprint NSF-ITP-96-145, hep-th/9611050 (1996).
46. [46] L. Faddeev and L. Takhtajan, Hamiltonian methods in the theory of solitons (Springer, Berlin, 1987).