Poisson sigma model over group manifolds

Journal of Geometry and Physics

Volumn 54, Issue 2, 2005, Pages 173-196

  Bonechi, Francesco ^a   Zabzine, Maxim ^b  

^a INFN SEZIONE DI FIRENZE   (Italy)

^b LPTHE   (France)

Author keywords

D branes; Poisson sigma model; Poisson Lie structure

Indexed keywords

EID: 18144368468     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomphys.2004.09.004     Document Type: Article

References (30)

1. R. Abraham J.E. Marsden Foundations of Mechanics 1978 Benjamin/Cummings Publishing Co., Inc., Advanced Book Program Reading, MA xxii+m-xvi+806 pp
2. A.Y. Alekseev P. Schaller T. Strobl The topological G/G WZW model in the generalized momentum representation Phys. Rev. D 52 1995 7146 (arXiv:hEp-th/9505012)
3. M.F. Atiyah R. Bott The Yang-Mills equations over Riemann surfaces Phil. Trans. Roy. Soc. Lond. A 308 1982 523
4. M. Blau G. Thompson Topological gauge theories of antisymmetric tensor fields Ann. Phys. 205 1991 130
5. M. Bojowald T. Strobl Classical solutions for Poisson sigma models on a Riemann surface JHEP 0307 2003 002 (arXiv:hEp-th/0304252)
6. F. Bonechi N. Ciccoli M. Tarlini Noncommutative instantons on the 4-sphere from quantum groups Commun. Math. Phys. 226 2002 419 (arXiv:mAth.qa/0012236)
7. I. Calvo F. Falceto D. Garcia-Alvarez Topological Poisson sigma models on Poisson-Lie groups JHEP 0310 2003 033 (arXiv:hEp-th/0307178)
8. A.S. Cattaneo G. Felder A path integral approach to the Kontsevich quantization formula Commun. Math. Phys. 212 2000 591 (arXiv:mAth.qa/ 9902090)
9. A.S. Cattaneo, G. Felder, Coisotropic Submanifolds in Poisson Geometry and Branes in the Poisson Sigma Model, Lett. Math. Phys. 67 (2004) 33-48 (arXiv:mAth.qa/0309180).
10. N. Ciccoli Quantization of coisotropic subgroups Lett. Math. Phys. 42 1997 123-138
11. P. De Bartolomeis Principal bundles in action Riv. Mat. Univ. Parma (4) 17 1991 1-65
12. V.G. Drinfeld, On Poisson homogeneous spaces of Poisson-Lie groups, Theoret. Mat. Fiz. 95 (2) (1993) 226 [Translation in Theoret. Math. Phys. 95 (2) (1993) 524].
13. F. Falceto K. Gawedzki Boundary G/G theory and topological Poisson-Lie sigma model Lett. Math. Phys. 59 2002 61 (arXiv:hEp-th/0108206)
14. V.L. Ginzburg A. Weinstein Lie-Poisson structure on some Poisson-Lie Groups J. Am. Math. Soc. 5 2 1992
15. G.T. Horowitz Exactly soluble diffeomorphism invariant theories Commun. Math. Phys. 125 1989 417
16. N. Ikeda Two-dimensional gravity and nonlinear gauge theory Ann. Phys. 235 1994 435 (arXiv:hEpth/9312059)
17. T.A. Ivanova A.D. Popov On symmetries of Chern-Simons and BF topological theories J. Nonlin. Math. Phys. 7 2000 48 (arXiv:hEp-th/9908177)
18. A.A. Kirillov Elements of the theory of representations Grundlehren der Mathematischen Wissenschaften, Band 220 1976 Springer-Verlag Berlin xi+315 pp
19. C. Klimcik P. Severa Dual nonAbelian duality and the Drinfeld double Phys. Lett. B 351 1995 455 (arXiv:hEp-th/9502122)
20. S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, vol. I (Reprint of the 1963 original), Wiley Classics Library, Wiley-Interscience/Wiley, New York, 1996, xii+329 pp.
21. M. Kontsevich, Deformation Quantization of Poisson Manifolds, Lett. Math. Phys. 66 (2003) 157-276 (arXiv:q-alg/9709040).
22. Y. Kosmann-Schwarzbach, Lie bialgebras, Poisson Lie groups and dressing transformations, Integrability of Nonlinear Systems (Pondicherry, 1996), Lecture Notes in Physics, vol. 495, Springer, Berlin, 1997, pp. 104-170.
23. J.-H. Lu A. Weinstein Poisson Lie groups, dressing transformations, and Bruhat decompositions J. Diff. Geom. 31 2 1990 501-526
24. J.-H. Lu, Multiplicative and affine Poisson structure on Lie groups, Ph.D. Thesis, University of California, Berkeley, 1990.
25. P. Schaller T. Strobl Poisson structure induced (topological) field theories Mod. Phys. Lett. A 9 1994 3129 (arXiv:hEp-th/9405110)
26. C. Schweigert On moduli spaces of flat connections with non-simply connected structure group Nucl. Phys. B 492 1997 743 (arXiv:hEp-th/ 9611092)
27. M.A. Semenov-Tian-Shansky Dressing transformations and Poisson group actions Publ. Res. Inst. Math. Sci. 21 6 1985 1237-1260
28. I. Vaisman Lectures on the geometry of Poisson manifolds Progress in Mathematics vol. 118 1994 Basel viii+205 pp
29. M.A. Vasiliev Consistent equations for interacting massless fields of all spins in the first order in curvatures Ann. Phys. 190 1989 59
30. A. Weinstein Coisotropic calculus and Poisson groupoids J. Math. Soc. Jpn. 40 4 1988 705-727